MCQs of Differential Equations

Showing 51 to 60 out of 145 Questions

51.

If the differential equationn representing the family of all circles touching x- axis at the origin is

(x^{2} - y^{2}) \frac{d y}{d x} = g (x) y

then g(x) equals.

52.

If \frac{d y}{d x} + y \tan x = \sin 2 x

and y(0) = 1, then y(π) is equal to _____

53.

The general solution of the differential equation,

\sin 2 x (\frac{d y}{d x} - \sqrt{\tan x}) - y = 0

is :

54.

If y(x) is the solution of the differential equation

(x + 2) \frac{d y}{d x} = x^{2} + 4 x - 9, x \neq - 2

and y(0) = 0, then y(-4) is equal to :

55.

The solution of the differential equation

y d x - (x + 2 y^{2}) d y = 0

is x = f(y) :

56.

The solution of the differential equation

\frac{d y}{d x} + \frac{y}{2} s e c x = \frac{\tan x}{2 y}

, where

0 \leq x \leq \frac{π}{2}

, and y(0) = 1, is given by :

57.

The order and degree of differential equation of

{[1 + {(\frac{d y}{d x})}^{2}]}^{\frac{3}{2}} = k \frac{d^{2} y}{d x^{2}}

are respectively _____ and _____

58.

The differential equation whose solution is the curves of system y = a cos ωt + b sin ωt is _____ .

59.

Solution of a differential equation

\frac{d x}{x} = \frac{y d y}{1 + y^{2}}

, y(1) = 0 represents _____

60.

The solution of the differential equation

\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}

is _____

Showing 51 to 60 out of 145 Questions