If u(x) and u(x) are two independent solutions of the differentia

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

21.

If y = cos-1x, then it satisfies the differential equation

1 - x2d2ydx2 - xdydx = c, where c equal to 

  • 0

  • 3

  • 1

  • 2


22.

The solution of the differential equation ydydx = xy2x2 + ϕy2x2ϕ'y2x2 is (where, c is a constant)

  • ϕy2x2 = cx

  • y2x2 = c

  • ϕy2x2 = cx2

  • x2ϕy2x2 = c


23.

The curve y = cosx + y1/2 satisfies the differential equation

  • 2y - 1d2ydx2 + 2dydx2 + cosx = 0

  • d2ydx2 + 2dydx2 + cosx = 0

  • 2y - 1d2ydx2 -  2dydx2 + cosx = 0

  • 2y - 1d2ydx2 - dydx2 + cosx = 0


24.

The solution of the differential equation

dydx + yxlogex = 1x

under the condition y = 1 when x = e is

  • 2y = logex +1logex

  • y = logex +2logex

  • ylogex = logex +1

  • y = logex +e


Advertisement
Advertisement

25.

If u(x) and u(x) are two independent solutions of the differential equation

d2ydx2 + b dydx + cy = 0,

then additional solution(s) of the given differential equation is(are)

  • y = 5u(x) + 8v(x)

  • y = c1{u(x) - v(x)} + c2v(x), c1 and c2 are arbitrary constants

  • y = c1u(x)v(x) + c2u(x)v(x), c1 and c2 are arbitrary constant

  • y = u(x)v(x)


A.

y = 5u(x) + 8v(x)

B.

y = c1{u(x) - v(x)} + c2v(x), c1 and c2 are arbitrary constants

We know that u(x) and v(x) are two independent solutions of the given differential equation, then their linear combination is also the solution of the given equation.

Here, we see that y = 5u(x) + 8v(x) is a linear combination and y = c1{u(x) - v(x)} + c2v(x) is also a linear combination of two independent solutions


Advertisement
26.

The solution of the differential equation y2 + 2xdydx = y satisfies x = 1, y = 1. Then, the solution is

  • x = y21 + logey

  • y = x21 + logex

  • x = y21 - logey

  • y = x21 + logex


27.

A family of curves is such that the length intercepted on the y-axis between the origin and the tangent at a point is three times the ordinate of the point of contact. The family of curves is

  • xy = C, C is a constant

  • xy2 = C, C is a constant

  • x2y = C, C is a constant

  • x2y2 = C, C is a constant


28.

The solution of the differential equation ysinxydx = xsinxy - ydy satisfying yπ4 = 1 is

  • cosxy = logey + 12

  • sinxy = logey + 12

  • sinxy = logex - 12

  • cosxy = - logex - 12


Advertisement
29.

The general solution of the differential equation

dydx = x +y +12x +2y +1 is

  • loge3x + 3y + 2 + 3x + 6y = C

  • loge3x + 3y + 2 - 3x + 6y = C

  • loge3x + 3y + 2 - 3x - 6y = C

  • loge3x + 3y + 2 + 3x - 6y = C


30.

Let y be the solution of the differential equation

xdydx = y21 - ylogx satisfying y(1) = 1. Then, y satisfies

  • y = xy - 1

  • y = xy

  • y = xy + 1

  • y = xy + 2


Advertisement