Important Questions of Differential Equations Mathematics | Zigya

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 Multiple Choice QuestionsMultiple Choice Questions

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401.

Let y = y(x) be the solution of the differential equation,  xy'  y = x2(xcosx + sinx), x > 0. If y(π) = π, then  y''π2 + yπ2 is equal to :

  • 1 + π2

  • 1 + π2 + π24

  • 2 + π2 +π24

  • 2 + π2


402.

If a + 2bcosxa - 2bcosy = a2 - b2, where a > b, then dxdy at π4, π4 is :

  • 2a + b2a - b

  • a + ba - b

  • a - ba + b

  • a - 2ba + 2b


 Multiple Choice QuestionsShort Answer Type

403.

Suppose a differentiable function f(x) satisfies the identity f(x + y) = f(x) + f(y) + xy2 + x2y, for all real x and y. If

limx0fxx = 1, then f'(3) is equal to :


 Multiple Choice QuestionsMultiple Choice Questions

404.

The solution of the differential equation dydx - y + 3xlogey + 3x + 3 = 0 is(where C is a constant of integration)

  • x - 2logey + 3x = C

  • x - logey = 3x = C

  • y + 3x - 12logex2 = C

  • y - 12logey + 3x2 = C


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405.

If y = y(x) is the solution of the differential equation 5 + ex2 + ydydx ex = 0 satisfyingy0 = 1, then a value of yloge13 is :

  •  - 1

  • 0

  • 2

  • 1


406.

Let y = yx be the solution of the differential equationcosxdydx + 2ysinx = sin2x, x  0, π2If yπ/3 = 0, then yπ/4 = ?

  • 12 - 1

  • 2 - 2

  • 2 - 2

  • 2 + 2


407.

If y = 2πx - 1csc(x) is the solution of the differential equation, dydx + pxy = 2πcscx, 0 < x < π2 then the function p(x) is equal to:

  • tanx

  • cscx

  • cotx

  • secx


408.

Let z = x + iy be a non-zero complex number such that z2 = i |z|2, where i =  - 1, then z lies on the:

  • real axis

  • line y = x

  • line y = - x

  • imaginary axis


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