JEE Questions for Maths Differential Equations Quiz 4

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An integrating factor of the differential equation
Maths-Differential Equations-22902.png

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If y(x) satisfies the differential equation y ' - y tan x = 2 x sec x and y (= 0, then

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x = y3 + Cy
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x = y2 + Cy
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x3 = y3 + Cy
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None of these

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An integrating factor of the differential equation (1 + x²) dy/dx + xy = x is

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x

Integrating factor (IF) of the differential equation
Maths-Differential Equations-22922.png

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The solution of y dx - x dy + log x dx = 0 is

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y - log x - 1 = Cx
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x + log y + 1 = Cx
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y + logx + 1 = Cx
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y + log x - 1 = Cx

Solution of the differential equations
cos x dy = y (sin x - y)dx, 0 < x < π/2, is

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sec x = (tan x + C) y
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y sec x = tan x + C
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y tan x = sec x + C
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tan x = (sec x + C)y

The equation of one of the curves whose slope at any point is equal to y + 2x is

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y = 2(ex + x - 1)
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y = 2(ex - x - 1)
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y = 2(ex - x + 1)
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y = 2(ex + x + 1)

The solution of the differential equation
Maths-Differential Equations-22927.png

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y = - x2 - 2x - 2 + Cex
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y = x2 + 2x + 2 - Cex
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x = - y2 - 2y + 2 - Cey
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x = - y2 - 2y - 2 + Cey
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x = y2 + 2y + 2 - Cey

The solution of the differential equation
Maths-Differential Equations-22929.png

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The solution of the differential equation
Maths-Differential Equations-22934.png

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The solution of the differential equation
Maths-Differential Equations-22939.png

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y = x log x + x
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y = log x + x
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y = x log x + x2
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y = xe(x - 1)

The solution of the differential equation
Maths-Differential Equations-22940.png

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y = x3 (ex - e)
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y = x3 (e - ex)
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y = x2 (ex - e)
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y = x2 (e - ex)

The integrating factor of the differential equation
Maths-Differential Equations-22941.png

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The solution of the differential equation
Maths-Differential Equations-22947.png

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The solution of the differential equation
Maths-Differential Equations-22952.png

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The solution of the differential equation
Maths-Differential Equations-22962.png

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To reduce the differential equation
Maths-Differential Equations-22967.png

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The solution of the differential equation
Maths-Differential Equations-22972.png

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An integrating factor of the differential equation (1 + y + x² y) dx + (x + x³)dy = 0 is

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log x
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x
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ex
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1/x
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- (1/x)

The solution of differential equation
Maths-Differential Equations-22977.png

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The solution of the differential equation
Maths-Differential Equations-22988.png

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Both I and II is correct
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Neither I nor II is incorrect
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I is correct, II is incorrect
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I is incorrect, II is correct

Let the population of rabbits surviving at a time t be governed by the differential equation
Maths-Differential Equations-22999.png

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400 - 300et/2
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300 - 200et/2
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600 - 500et/2
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400 - 300e-t/2

The equation of the curve for which the square of the ordinate is twice the rectangle contained by the abscissa and the intercept of the normal on X - axis and passing through (2,is

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x2 + y2 - x = 0
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4x2 + 2y2 - 9y = 0
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2x2 + 4y2 - 9x = 0
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4x2 + 2y2 - 9x = 0

A gardener is digging a plot of land. As he gets tried, he works more slowly. After t min, he is digging at a rate of 2/√t m²/min. How long will take him to digging an area of 40 sqm ?

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100 min
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10 min
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30 mm
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40 min

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A present, a firm is manufacturing 2000 items, It is estimated that the rate of change of production P with respect to additional number of workers x is given by dp/dx = 100 - 12√x. If the firm employees 25 more workers, then the new level of production of item is

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2500
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3000
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3500
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4500

For the population p(t) at time t of a certain mouse species, the differential equation
Maths-Differential Equations-23011.png

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2 log 18
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log 9
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1/2 log 18
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log 18

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The equation of the curve whose tangent at any point (x, y) makes an angle tan^-1 (2x + 3y) with X - axis and which passes through (1,is

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6x + 9y + 2 = 26e3(x - 1)
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6x - 9y + 2 = 26e3(x - 1)
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6x + 9y - 2 = 26e3(x - 1)
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6x - 9y - 2 = 26e3(x - 1)

The equation of the curve satisfying the equation (xy - x²)dy/dx = y² and passing through the point (-1,is

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y = (log y - 1)x
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y = (log y + 1)x
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x = (log x - 1)y
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x = (log x + 1)y

The slope at any point of a curve y = f(x) is given by dy/dx = 3x² and it passes through (-1, 1). The equation of the curve is

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y = x3 + 2
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y = -x - 2
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y = 3x3 + 4
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y = -x3 + 2

A curve having the condition that the slope of tangent at some point is two times the slope of the straight line joining the same point to the origin of coordinates, is a/an

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circle
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ellipse
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parabola
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hyperbola

The equation of the curve satisfying the differential equation y₂(x² += 2xy₁ passing through the point (0,and having slope of tangent at x = 0 as 3 is