MCQs of Differential Equations

Showing 31 to 40 out of 100 Questions

31.

The general solution of

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

is _____

32.

The integrating factor of

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

is _____

33.

The integrating factor of

(1 + x) \frac{d y}{d x} - x y = 1 - x

is _____

34.

The equation of curve passing through (2, 1) and slope of tangent at (x, y) is

\frac{x^{2} + y^{2}}{2 x y}

35.

The solution of the equation

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

36.

The solution of the differential equation

(1 + y^{2}) + (x - e^{\tan^{- 1} y}) \frac{d y}{d x} = 0

37.

(t + 1) \frac{d y}{d x} - t y = 1

and y(0) = -1 then y(1) = _____

38.

The solution of the differential equation

\frac{d y}{d x} = \frac{x + y}{x}

satisfying the condition y(1) = 1 is

39.

If a curve passes through the point

(2, \frac{7}{2})

and has slope

(1 - \frac{1}{x^{2}})

at any point (x, y) on it, then the ordinate of the point on the curve whose abscissa is -2 is :

40.

The equation of the curve passing through the origin and satisfying the differential equation

(1 + x^{2}) \frac{d y}{d x} + 2 x y = 4 x^{2}

is :

Showing 31 to 40 out of 100 Questions