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JEE Questions for Maths Differential Equations Quiz 3 - MCQExams.com
JEE
Maths
Differential Equations
Quiz 3
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n2 y
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-n2 y
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-y
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2x2 y
The solution of the differential equation
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y = log x + C
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y2 = (log x)2 + C
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y = log x + xy
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xy = xy + C
A solution of the differential equation
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y = 2x
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y = - 2x
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y = 2x - 4
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y = 2x + 4
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y = x (log x -+ 4
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y = x (log x - 1)+3
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y = x (log x ++ 1
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y = x (log x -+ 1
The solution of the differential equation
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2)
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Solution of the differential equation
x
dy - yd
x
= 0 represents a
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parabola
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circle
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hyperbola
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straight line
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a = b
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a = -b
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a = - 2b
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a = 2b
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2)
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The solution of differential equation (1 +
x
)y d
x
+ (1 - y)
x
dy = 0 is
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loge (xy) + x - y = C
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2)
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loge (xy) - x + y = C
The solution of the differential equation
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2)
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The solution of the equation
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y = C (x + a)(1 - ay)
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y = C (x + a)(1 + ay)
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y = C(x - a)(1 + ay)
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None of these
The solution of the differential equation
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2)
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The differential equation (e
x
+ 1)y dy = (y + 1)e
x
d
x
, has the solution
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(y - 1)(ex -= Cey
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(y - 1)(ex += C ey
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(y + 1)(ex -= Cey
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(y + 1)(ex += Cey
The solution of the differential equation
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2(x - y) + log (x - y) = x + C
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2(x - y) - log (x - y += x + C
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2(x - y) + log (x - y += x + C
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None of the above
The differential equation y (dy/d
x
) +
x
= c represents
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a family of hyperbolas
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a family of circles whose centres are on the Y - axis
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a family of parabolas
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a family of circles whose centres are on the X -axis
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2)
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The solution of the differential equation
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2)
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The solution of the differential equation
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2)
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None of these
The solution of the differential equation 9y (dy/d
x
) + 4
x
= 0 is
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2)
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0%
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1
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1/4
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1/2
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2
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(x - 2y)2 + 2x = C
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(x - 2y)2 + x = C
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(x - 2y) + 2x2 = C
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(x - 2y) + x2 = C
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(1 + x(1 + y= C
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(1 + x2)(1 + y= Cx2
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(1 - x(1 - y= C
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(1 + x(1 + y= Cy2
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variable radii and a fixed centre (0, 1)
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variable radii and a fixed centre (0, -1)
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fixed radius 1 and variable centres along the X - axis
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fixed radius 1 and variable centres along the Y - axis
The equation of curve through point (1,which satisfies the differential equation (1 + y
2
) d
x
-
x
y dy = 0, is
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x2 + y2 = 4
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x2 - y2 = 1
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2x2 + y2 = 2
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None of these
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2)
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The solution of the differential equation sec
2
x
tan y d
x
+ sec
2
y tan
x
dy = 0 is
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tan y tan x = C
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2)
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None of these
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2)
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x + y = a
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2)
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x2 + y2 = a2
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If C is an arbitrary constant, then the general solution of the differential equation y d
x
-
x
dy =
x
yd
x
is given by
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y = Cxe-x
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y = Cye-x
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y + ex = Cx
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yex = Cx
The real value of m for which the substitution y = u
m
will transform the differential equation
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m = 0
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m = 1
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m = 3/2
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m = 2/3
The solution of the differential equation
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2)
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ey/x + log x = 1
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e-y/x = log x
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e-y/x + 2 log x = 1
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e-y/x + log x = 1
The solution of the differential equation (
x
2
- y
2
) d
x
+ 2
x
y dy = 0 is
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x2 - y2 = Cx
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x2 - y2 = Cy
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x2 + y2 = Cx
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x2 + y2 = Cy
The solution of the equation (
x
2
+
x
y)dy = (
x
2
+ y
2
)d
x
is
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2)
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None of these
The general solution of the differential equation
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loge |3x + 3y + 2|+ 3x + 6y = C
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loge |3x + 3y + 2|- 3x + 6y = C
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loge |3x + 3y + 2|- 3x - 6y = C
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loge |3x + 3y + 2|+ 3x - 6y = C
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2)
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None of the above
The solution of the differential equation
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2)
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The solution of the differential equation (3
x
y + y
2
)d
x
+ (
x
2
+
x
y)dy = 0 is
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x2 (2xy + y= C2
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x2 (2xy - y= C2
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x2(y2 - 2xy= C2
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None of these
The solution of the differential equation
x
y
2
dy - (
x
3
+ y
3
)d
x
= 0 is
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y3 = 3x3 + C
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y3 = 3x3 log (Cx)
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y3 = 3x3 + log (Cx)
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y3 + 3x3 = log (Cx)
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2)
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The general solution of y
2
d
x
+ (
x
2
-
x
y +y
2
)dy = 0 is
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2)
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The solution of the differential equation (
x
2
+ y
2
)d
x
= 2
x
y dy is
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x2 + y2 = Cy
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C(x2 - y= x
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x2 - y2 = Cy
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x2 + y2 = Cx
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2)
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If d
x
+ dy = (
x
+ y) (d
x
- dy), then log (
x
+ y) is equal to
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x + y + C
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x + 2y + C
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x - y + C
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2x + y + C
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Cx2
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Cx
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Cx3
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Cx4
The general solution of the differential equation
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2)
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The integrating factor of the differential equation
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tan-1 x
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1 + x2
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etan-1 x
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loge (1 + x2)
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2)
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If
f
(
x
) is differentiable on the interval (0, ∞) such that
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2)
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Which of the following is a correct solution of
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2)
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