MCQs of Differential Equations

Showing 81 to 90 out of 100 Questions

81.

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

is a general solution of differential equation

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

, then its particular solution for the initial condition y(1) = 2 is _____.(where c is an arbitrary constant)

82.

General solution of the differential equation (tanx) dx + (tany) dy = 0 is _____.

83.

For the differential equation

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

, taking

\frac{y}{x} = v

,its variable separable form in the variable v and x is _____.

84.

The numbers of arbitrary constants in the particular solution of a differential equation having order and degree 2 and 3 respectively is _____ .

85.

The particular solution of differential equation

\frac{d y}{d x} = - 4 x y^{2}, y (0) = 1

is _____ .

86.

Integrating Factor of differential equation

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

is _____.

87.

The degree of the differential equation

{(y_{2})}^{2} - \sqrt{y_{1}} = y^{3}

is _____ .

88.

The integrating factor of the differential equation

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

is _____ .

89.

The integrating factor for the differential equation

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

is _____.

90.

The particular solution of the differential equation

\log {}_{e}{(\frac{d y}{d x})} = 3 x + 4 y, y (0) = 0

is _____.

Showing 81 to 90 out of 100 Questions