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CBSE Questions for Class 12 Commerce Maths Differential Equations Quiz 10 - MCQExams.com
CBSE
Class 12 Commerce Maths
Differential Equations
Quiz 10
Solution of the differential equation
{
1
x
−
y
2
(
x
−
y
)
2
}
d
y
+
{
y
2
(
x
−
y
)
2
−
1
y
}
d
x
=
0
is
Report Question
0%
ln
|
x
y
|
+
x
y
x
−
y
=
c
0%
x
y
x
−
y
=
c
e
x
/
y
0%
ln
|
x
y
|
=
c
+
x
y
x
−
y
0%
n
o
n
e
o
f
t
h
e
s
e
The solution of the differential equation
x
2
d
y
d
x
cos
(
1
x
)
−
y
sin
(
1
x
)
=
−
1
;
w
h
e
r
e
y
→
−
1
a
s
x
→
∞
is
Report Question
0%
y
=
sin
(
1
x
)
−
cos
(
1
x
)
0%
y
=
x
+
1
x
sin
(
1
x
)
0%
y
=
cos
(
1
x
)
+
sin
(
1
x
)
0%
y
=
x
+
1
x
cos
(
1
x
)
Explanation
x
2
d
y
d
x
c
o
s
(
1
x
)
−
y
s
i
n
(
1
x
)
=
−
1
d
y
d
x
−
y
x
2
t
a
n
(
1
x
)
=
−
1
x
2
c
o
s
(
1
x
)
d
y
d
x
+
(
−
1
x
2
t
a
n
(
1
x
)
)
y
=
−
1
x
2
c
o
s
(
1
x
)
I
.
F
=
e
∫
−
1
x
2
t
a
n
(
1
x
)
d
x
1
x
=
t
−
d
x
x
2
=
d
t
=
e
∫
t
a
n
(
t
)
d
t
=
e
l
n
(
s
e
c
t
)
=
s
e
c
(
1
x
)
s
e
c
(
1
x
)
.
y
=
∫
1
x
2
c
o
s
(
1
x
)
.
s
e
c
(
1
x
)
=
−
∫
s
e
c
2
(
1
x
)
x
2
Let
1
x
=
t
−
d
x
x
2
=
d
t
=
∫
s
e
c
2
(
t
)
d
t
s
e
c
(
1
x
)
.
y
=
t
a
n
(
1
x
)
+
C
1.
−
1
=
0
+
C
C
=
−
1
s
e
c
(
1
x
)
.
y
=
t
a
n
(
1
x
)
−
1
,
y
=
s
i
n
(
1
x
)
−
c
o
s
(
1
x
)
The solution of the differential equation
d
y
d
x
=
x
2
+
y
2
+
1
2
x
y
satisfying
y
(
1
)
=
1
, is
Report Question
0%
a hyperbola
0%
a circle
0%
y
2
=
x
(
1
+
x
)
−
10
0%
(
x
−
2
)
2
+
(
y
−
3
)
2
=
5
Explanation
d
y
d
x
=
x
2
+
y
2
+
1
2
x
y
2
y
d
y
d
x
=
x
+
y
2
x
+
1
x
2
y
d
y
d
x
−
y
2
x
=
x
+
1
x
y
2
=
u
=
2
y
d
y
d
x
=
d
u
d
x
d
u
d
x
−
u
x
=
x
+
1
x
d
u
d
x
+
P
u
=
Q
1
x
d
u
d
x
−
u
x
2
=
1
+
1
x
2
∫
d
(
u
x
)
=
∫
(
1
+
1
x
2
)
d
x
⇒
u
x
x
−
x
−
1
+
C
⇒
y
2
x
=
x
−
1
x
+
C
⇒
y
2
=
x
2
−
1
+
x
The general solution of differential equation
d
y
d
x
=
sin
3
x
cos
2
x
+
x
e
x
Report Question
0%
y
=
1
5
cos
5
x
+
1
3
c
s
c
3
x
+
(
x
+
1
)
e
x
+
c
0%
y
=
1
5
cos
5
x
−
1
3
c
s
c
3
x
+
(
x
−
1
)
e
x
+
c
0%
y
=
−
1
5
cos
5
x
−
1
3
c
s
c
3
x
−
(
x
−
1
)
e
x
−
c
0%
None of these
The value of
lim
x
→
∞
y(x) obtained from the differential equation
d
y
d
x
=
y
−
y
2
, where y(0) = 2 is
Report Question
0%
1
0%
-1
0%
0
0%
2
2
−
e
Explanation
d
y
d
x
=
y
−
y
2
y
(
0
)
=
2
d
y
y
−
y
2
=
d
x
−
d
y
y
2
−
y
=
d
x
−
d
y
y
2
(
1
2
)
2
−
2
×
1
2
y
−
1
4
=
d
x
d
y
(
y
−
1
2
)
2
−
(
1
2
)
2
=
−
d
x
1
2
×
1
2
ln
|
y
−
1
2
−
1
2
y
−
1
2
+
1
2
|
=
−
x
+
c
ln
(
y
−
1
y
)
=
x
+
c
Given
y
(
0
)
=
2
ln
(
2
−
1
2
)
=
C
C
=
ln
(
1
2
)
ln
(
y
−
1
y
)
=
−
x
+
ln
(
1
2
)
ln
(
y
y
−
1
)
=
x
+
ln
(
2
)
y
y
−
1
=
e
x
+
ln
(
2
)
y
−
1
y
=
1
e
x
+
ln
(
2
)
1
−
1
y
=
e
−
(
x
+
ln
(
2
)
)
1
y
=
1
−
e
−
(
x
+
ln
(
2
)
]
y
=
1
1
−
e
−
[
x
+
ln
(
2
)
]
lim
x
→
∞
1
1
−
e
−
∞
=
1
1
−
0
=
1
The solution of the differential equation
d
y
d
x
+
1
x
tan
y
=
tan
y
sin
y
x
2
is
Report Question
0%
1
x
cos
y
=
1
2
x
2
+
K
0%
1
x
cot
y
=
1
2
x
2
+
K
0%
1
x
csc
y
=
1
2
x
2
+
K
0%
1
x
cos
x
=
1
2
x
2
+
K
The solution of the differential equation
(
3
x
y
+
y
2
)
d
x
+
(
x
2
+
x
y
)
d
y
=
0
is
Report Question
0%
x
2
(
2
x
+
y
)
=
3
0%
y
2
(
2
x
+
y
)
=
3
0%
x
2
y
(
2
x
+
y
)
=
3
0%
x
2
y
(
2
x
+
3
)
=
9
The solution of the differential equation
(
x
2
+
1
)
d
y
d
x
+
y
2
+
1
=
0
,
is
[
i
f
y
(
0
)
=
1
]
Report Question
0%
y
=
2
+
x
2
0%
y
=
(
1
+
x
)
(
1
−
x
)
0%
y
=
x
(
x
−
1
)
0%
y
=
(
1
−
x
)
(
1
+
x
)
The solution of differential equation
d
y
d
x
=
x
(
2
ln
x
+
1
)
sin
y
+
y
cos
y
is
Report Question
0%
y
sin
y
=
x
ln
x
+
c
0%
y
sin
y
=
x
2
ln
x
+
c
0%
sin
y
=
x
2
ln
x
+
c
0%
y
cos
y
=
x
2
ln
x
+
c
Explanation
Equation of family of circle is
(
n
+
a
)
2
+
(
y
−
a
)
2
=
a
2
or
x
2
+
y
2
+
2
a
x
−
2
a
y
+
a
2
=
0
------(1)
Diffentiating , we get
2
n
+
2
y
d
y
d
x
+
2
a
−
2
a
d
y
d
x
=
0
⇒
x
+
y
d
y
d
x
=
a
(
d
y
d
x
−
1
)
⇒
a
=
x
+
y
y
1
y
1
−
1
where
y
1
=
d
y
d
x
Substituting the value of a in eq
(
1
)
and Simplifying
⇒
(
x
y
1
−
x
+
x
+
y
y
1
)
+
(
y
y
1
−
y
−
x
−
y
y
1
)
2
=
(
x
+
(
y
y
1
)
)
2
⇒
(
x
+
y
)
2
[
(
y
1
)
2
+
1
]
=
(
x
+
y
y
1
)
2
The given differential equation is :
d
y
d
x
=
x
(
2
log
x
+
1
)
∼
y
+
y
cos
y
⇒
(
sin
y
+
y
cos
y
)
d
y
=
x
(
2
log
x
+
1
)
d
x
⇒
∫
(
sin
y
+
y
cos
y
)
d
y
=
∫
x
(
2
log
x
+
1
)
d
x
integrating both sides
⇒
−
cos
y
+
y
sin
y
−
∫
sin
y
d
y
=
2
log
x
x
2
2
−
2
∫
1
x
x
2
2
d
x
+
x
2
2
⇒
−
cos
y
+
y
sin
y
+
cos
y
=
x
2
log
x
−
x
2
2
+
x
2
2
+
c
⇒
y
sin
y
=
x
2
log
x
+
c
.......(2)
It is given that when
y
=
π
2
,
x
=
1
So, putting
y
=
π
2
,
x
=
1
in eq (2),
⇒
π
2
sin
π
2
=
1.
log
1
+
c
⇒
c
=
π
2
Putting
c
=
π
2
in eq (2) we oftain
y
sin
y
=
x
2
log
x
+
π
2
The equation of a curve passing through the point (0, 0) and whose differential equation is
y
′
=
e
x
sin
x
is
Report Question
0%
2
y
−
1
=
e
x
(
sin
x
−
cos
x
)
0%
2
y
−
1
=
e
−
x
(
cos
x
−
sin
x
)
0%
2
y
+
1
=
e
−
x
(
cos
x
−
sin
x
)
0%
N
o
n
e
o
f
t
h
e
s
e
Explanation
given,
d
y
d
x
=
e
x
sin
x
d
y
=
e
x
sin
x
.
d
x
∫
d
y
=
∫
e
x
sin
x
.
d
x
→
integrating both sides.
d
e
t
,
∫
e
x
sin
x
d
x
=
I
−
−
−
−
(
1
)
y
=
∫
e
x
↓
f
(
x
)
sin
x
↓
g
(
x
)
d
x
=
I
Since,
∫
f
(
x
)
g
(
x
)
d
x
=
f
(
x
)
.
∫
g
(
x
)
d
x
−
∫
[
f
′
(
x
)
∫
g
(
x
)
d
x
]
d
x
∴
I=e^x.(-\cos x)-\displaystyle \int e^x.(-\cos x).dx
I=-e^x\cos x+\displaystyle \int \underset{f(x)}{\underset{\downarrow}{e^x}}.\underset{g(x)}{\underset{\downarrow}{\cos x}}\ dx
Now apply same formula as above
I=-e^x\cos x.+\left [e^x.\displaystyle \int \cos x.dx-\displaystyle \int (ex.\displaystyle \int \cos x.dx)dx\right]
I=-{ e }^{ x }.\cos { x } +\left[ { e }^{ x }.\sin { x } -\underbrace { \displaystyle \int { { e }^{ x }.\sin { x } .dx } }_{ \left( I \right) } \right]
I=-e^x\cos x+e^x\sin x-I+c
2y=e^x(\sin x-\cos x)+c
Since this curve passes through
(0,0)
therefore
2\times 0=e^0(\sin 0\cos 0)+c
c=1
\therefore \
equation of curve
2y=e^x(\sin x-\cos x)+1
(2y-1)=e^x(\sin x-\cos x)
Solution of the differential equation
ye^{x/y}dx=(xe^{\frac {x}{y}}+y^{2})dy(y \neq 0)
is ?
Report Question
0%
e^{x/y}=x+C
0%
e^{x/y}+x=C
0%
e^{y/x}=x+C
0%
e^{x/y}=y+C
Solution of differential equation
xdy=(y-{x}^{2}-{y}^{2})dx
is (where
c
is arbitrary constant)
Report Question
0%
y=x\cos{(c+x)}
0%
y=x\tan{(x-c)}
0%
y=x\csc{(c+x)}
0%
none of these
Let
y=y(x)
be the solution of the differential equation
(1-x^2)\dfrac{dy}{dx}-xy=1,x\in(-1,1)
if
y(0)=0
, then
y\left(\dfrac{1}{2}\right)
is equal to
Report Question
0%
\dfrac{\pi}{3\sqrt3}
0%
\dfrac{\pi}{\sqrt3}
0%
\dfrac{\pi}{6}
0%
\dfrac{\pi}{3}
If the general solution of the differential equation if
y'=\frac { y }{ x } +\Phi \left( \frac { x }{ y } \right)
, for some function
\Phi
, is given by
yin|cx|=x
, where c is an arbitrary constant, then
\Phi
(2) is equal to :
Report Question
0%
4
0%
\frac { 1 }{ 4 }
0%
-4
0%
-\frac { 1 }{ 4 }
(2y+xy^{3})dx+(x+x^{2}y^{2})dy=0
solution of differential equation is
Report Question
0%
3x^{2}y+x^{3}y^{2}=c
0%
3x^{2}y^{2}+xy^{2}=c
0%
yx^{2}+\dfrac{xy}{3}=c
0%
x^{2}y+\dfrac{x^{3}y^{3}}{3}=c
Solution of differential equation
{ x }^{ 6 }dy+3{ x }^{ 5 }ydx=xdy-2y\ dx
is
Report Question
0%
{ x }^{ 3 }y=\dfrac { y }{ { x }^{ 2 } } +C
0%
{ x }^{ 3 }y=\dfrac { 2y }{ { x }^{ 2 } } +C
0%
{ x }^{ 3 }{ y }^{ 2 }=\dfrac { y }{ { x }^{ 2 } } +C
0%
{ x }^{ 3 }=\dfrac { y }{ { x }^{ 2 } } +C
The solution of equation
\dfrac { dy }{ dx } =\dfrac { 1 }{ x+y+1 }
Report Question
0%
x={ ce }^{ y }-y-2
0%
y=x+{ ce }^{ y }-2
0%
x+{ ce }^{ y }-2-2=0
0%
y=x
Let
y=y(x)
be the solution of the differential equation
\sin x\dfrac {dy}{dx}+y\cos x=4x,x\ \in\ (0,\pi)
, if
y\left(\dfrac {\pi}{2}\right)=0
, then
y\left(\dfrac {\pi}{6}\right)
is equal to
Report Question
0%
-\dfrac {4}{9}\pi^{2}
0%
\dfrac {4}{9\sqrt {2}}\pi^{2}
0%
\dfrac {-8}{9\sqrt {2}}\pi^{2}
0%
-\dfrac {8}{9}\pi^{2}
Solution of the differential equation
dr=a\left( r\sin\theta d\theta-\cos\theta dr \right )
is
Report Question
0%
r\left( 1+a\cos { \theta } \right) =c
0%
r\left( 1+a\cos { \theta } \right) =ac
0%
r\left( 1-a\cos { \theta } \right) =c
0%
r\left( 1-a\cos { \theta } \right) =ac
The solutions of the differential equation
\frac{dy}{dx}= \frac{siny+x}{sin2y-x cos y }
is
Report Question
0%
sin^{2}y = xsin y +\frac{x^{2}}{2}+c
0%
sin^{2}y = xsin y -\frac{x^{2}}{2}+c
0%
sin^{2}y = x+sin y +\frac{x^{2}}{2}+c
0%
sin^{2}y = x-sin y +\frac{x^{2}}{2}+c
The general solution of the differential equation
\dfrac{dy}{dx} + \sin \dfrac{x+y}{2} = \sin \dfrac{x-y}{2}
is
Report Question
0%
\log \left(\tan \dfrac{y}{2}\right) = c-2\sin x
0%
\log\left( \tan \dfrac{y}{4}\right) = c-2\sin \left(\dfrac{x}{2}\right)
0%
\log \left(\tan \left(\dfrac{y}{2} +\dfrac{\pi}{4}\right) \right)= c-2 \sin x
0%
None of the above
If
y\left(x\right)
is the solution of the differential equation
\left(x+2\right)\dfrac{dy}{dx}=x^{2}+4x-9,x\neq -2
and
y\left(0\right)=0
, then
y\left(-4\right)
is equal to
Report Question
0%
0
0%
1
0%
-1
0%
2
The solution of differential equation,
\left(x+\tan y\right)dy=\sin 2y\,dx
is
Report Question
0%
xcoty=\dfrac{1}{2}\log |cosec2y-cot2y|+c
0%
x=\tan y+c\sqrt{\tan y}
0%
x=\cot y+c\sqrt{\cot y}
0%
None\ of\ these
If a curve
y=f(x)
passes through the point
(1,-1)
and satisfies the differential equation,
y(1+xy)dx=xdy
, then
f\left(-\dfrac {1}{2}\right)
is equal to
Report Question
0%
-\dfrac {4}{5}
0%
\dfrac {2}{5}
0%
\dfrac {4}{5}
0%
-\dfrac {2}{5}
General solution of differential equation
x^{2}(x+y\frac{dy}{dx})+(x\frac{dy}{dx}-y)\sqrt{x^{2}+y^{2}}=0
is
Report Question
0%
\frac{1}{\sqrt{x^{2}+y^{2}}}+\frac{y}{x}=c
0%
\sqrt{x^{2}+y^{2}}-\frac{y}{x}=c
0%
\sqrt{x^{2}+y^{2}}+\frac{y}{x}=c
0%
2\sqrt{x^{2}+y^{2}}+\frac{y}{x}=c
0%
\frac{1}{\sqrt{x^{2}+y^{2}}}-\frac{y}{x}=c
Solution of the differential equation
\dfrac{dy}{dx}=\dfrac{y(1+x)}{x(y-1)}
is
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0%
\log|xy|+x-y=C
0%
\log|xy|-x+y=C
0%
\log|xy|+x+y=C
0%
\log|xy|-x-y=C
Solution of
(x+y-1)dx+(2x+2y-3)dy=0
is
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0%
y+x+log(x+y-2)=c
0%
y+2x+log(x+y-2)=c
0%
2y+x+log(x+y-2)=c
0%
2y+2x+log(x+y-2)=c
The solution of
\dfrac{xdy}{x^{2}+y^{2}}=\left(\dfrac{y}{x^{2}+y^{2}}-1\right)dx
is
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0%
y=x\cot(c-x)
0%
\cos^{-1}u/x=-x+C
0%
y=x\tan (c-x)
0%
y^{2}/x^{2}=x\tan (c-x)
General solution of differential equation
x^2dy + y(x + y)dx = 0
is
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0%
2x + y = Ax^2Y
0%
2x - y = \dfrac{Ax^2}{y}
0%
2x + y = \dfrac{Ax^2}{y}
0%
x - 2y = Ax^2y
If
y(t)
is solution of
(t + 1) \dfrac{dy}{dt} - ty = 1, y(0) = -1
, then
y(1) =
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0%
\dfrac{1}{4}
0%
-2
0%
-\dfrac{1}{2}
0%
\dfrac{1}{2}
Solution of the differential equation
\cos{\,}x {\,}dy=y(\sin{\,}x-y)dx,0<x<\dfrac{\pi}{2}
is
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0%
y sec x
=
tan x
+
c
0%
y sec x
=
sec x
+
c
0%
y sec x
=
(sec x
+
c) y
0%
sec x
=
y (tan x
+
c)
The solution of the differential equation
ydx-xdy+3x^2y^2e^{x^3} dx=0
is
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0%
\dfrac{x}{y}+e^{x^3}=c
0%
\dfrac{x}{y}-e^x=c
0%
\dfrac{x}{y}+ex^{x^3}-x^2y=c
0%
\dfrac{x}{y}-e^{x^3}=c
Solution of the equation
(x+y)^2\dfrac{dy}{dx}=4,y(0)=0
is
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0%
y=2tan^{-1}\left(\dfrac{x+y}{2}\right)
0%
y=4tan^{-1}\left(\dfrac{x+y}{4}\right)
0%
y=4tan^{-1}\left(\dfrac{x+y}{2}\right)
0%
y=2tan^{-1}\left(\dfrac{x+y}{4}\right)
The solution of the differential equation
\log\left(\dfrac {dy}{dx}\right)=4x-2y-2,y=1
when
x=1
is
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2e^{2y+2}=e^{4x}+e^{2}
0%
2e^{2y-2}=e^{4x}+e^{2}
0%
2e^{2y+2}=e^{4x}+e^{4}
0%
3e^{2y+2}=e^{3x}+e^{2}
the solution of
ydx-xdy+3{ x }^{ 2 }{ y }^{ 2 }{ e }^{ { x }^{ 3 } }dx=0
is
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0%
\frac { x }{ y } +{ e }^{ { x }^{ 3 } }
=C
0%
\frac { x }{ y } -{ e }^{ { x }^{ 3 } }
=0
0%
-\frac { x }{ y } +{ e }^{ { x }^{ 3 } }
=C
0%
none of these
The solution of the differential equation
\left(x+2y^{3}\right)\dfrac{dy}{dx}=y
is
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0%
\dfrac{x}{y^{2}}=y+C
0%
\dfrac{x}{y}=y^{2}+C
0%
\dfrac{x^{2}}{y}=y^{2}+C
0%
\dfrac{x}{y}=x^{2}+C
General solution of the differential equation (x+y-2) dy=(x+y) dx is
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0%
y+x=log(y-x+1)+c
0%
y-x log (x+y-1)+c
0%
y-2x=log (x+y-1)+c
0%
y+2x=log (x+y+1)+c
The solution of
x^2dy-y^2dx+xy^2(x-y)dy=0
is?
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0%
ln\left|\dfrac{x-y}{xy}\right|=\dfrac{y^2}{2}+c
0%
ln\left|\dfrac{xy}{x-y}\right|=\dfrac{x^2}{2}+c
0%
ln\left|\dfrac{x-y}{xy}\right|=\dfrac{x^2}{2}+c
0%
ln\left|\dfrac{x-y}{xy}\right|=x+c
Solution of
\left(1+xy\right)ydx+\left(1-xy\right)xdy=0
is
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0%
\log\dfrac{x}{y}+\dfrac{1}{xy}=c
0%
\log\dfrac{x}{y}=c
0%
\log\dfrac{x}{y}-\dfrac{1}{xy}=c
0%
\log\dfrac{y}{x}-\dfrac{1}{xy}=c
The general solution of the differential equation
y-x\dfrac{dy}{dx}=y^{2}\cos x\left(1-\sin x\right)
is
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0%
y\left(\sin x+c\right)=\tan x+\sec x
0%
y\left(\sin x+c\right)=\tan x-\sec x
0%
\dfrac{x}{y}=\sin x+\dfrac{1}{4}\cos 2x+c
0%
\dfrac{x}{y}=\sin x+\dfrac{1}{8}\cos 2x+c
Solution of
\dfrac { d y } { d x } + 2 x y = y
is
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0%
y = c e ^ { x - x ^ { 2 } }
0%
y = c e ^ { x ^ { 2 } } - x
0%
y = c e ^ { x }
0%
y = c e ^ { - x ^ { 2 } }
Let =y(x) be the solution of the differential equation, x
\frac { dy }{ dx } +y=x{ log }_{ e }x,(x>1).
If
2y(2)={ log }_{ e }4-1,
then y(e) is equal to :
Report Question
0%
-\dfrac { { e }^{ 2 } }{ 2 }
0%
\dfrac { e } { 4 }
0%
\dfrac { { e }^{ 2 } }{ 4 }
0%
-\dfrac { { e }^{ 2 } }{ 4}
The solution of the Differential Equation
(x+y)(dx-dy)=dx+dy
is
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0%
l\ n(x-y)=x+y+C
0%
l\ n(x+y)=x-y+C
0%
l\ n(x-y)=x-y-C
0%
none\ of\ these
The integrating factor of the equation
y^{2}dx+(3xy-1)dy=0
is
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0%
y^{2}
0%
y^{3}
0%
\dfrac {1}{y^{2}}
0%
\dfrac {1}{y^{3}}
The solution of the differential equation
\dfrac{dy}{dx}=\sec (x+y)
is
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0%
y-\tan\dfrac{x+y}{2}=c
0%
y+\tan\dfrac{x+y}{2}=c
0%
y+2\tan\dfrac{x+y}{2}=c
0%
None\ of\ these
The solution of differential equation
dy/dx -y/x+\tan y/x
is:
Report Question
0%
x=C'\cos (y/x)
0%
x=C'\sin (y/x)
0%
x=C'\csc (y/x)
0%
none\ of\ these
The solution of the equation
\dfrac{dy}{dx}=\dfrac{(1+x)y}{(y-1)x}
is:
Report Question
0%
\log xy+x+y=c
0%
\log (\dfrac{x}{y})+x-y=c
0%
y-x-\log xy=c
0%
None\ of\ these
Solution of
\left(\dfrac {dy}{dx}\right)^{2}+x\dfrac {dy}{dx}-y=0
is
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0%
y=3x^{2}+9
0%
y=3x+9
0%
y=\dfrac {4}{3}x^{2}
0%
y=9x+3
Number of values of m
\in
N, for which
y=e^{mx}
is a solution of the differential equation
D^3y-3D^2y-4Dy+12y=0
, is?
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0%
0
0%
1
0%
2
0%
More than
2
The solution the differential equation
\left(\dfrac{dy}{dx}\right)^{2}-\dfrac{dt}{dx}(e^{x}+e^{-x})+1=0
is/are
Report Question
0%
y+e^{-x}=c
0%
y-e^{-x}=c
0%
y+e^{x}=c
0%
y-e^{x}=c
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Practice Class 12 Commerce Maths Quiz Questions and Answers
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