MCQs of Differential Equations

Differential Equations MCQs

MCQs of Differential Equations

Showing 101 to 110 out of 145 Questions

101.

The general solution of differential equation

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

is _____ .

(a)	cx - y - 2 = 0
(b)	cx + y + 2 = 0
(c)	cx + y - 2 = 0
(d)	cx + x - 2 = 0

102.

The order and degree of the differential equation

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

are ______ respectively.

(a)	4, 4
(b)	2, 4
(c)	4, 2
(d)	2, 2

103.

The family of curves is represented by y = a cos^-1x + b, where a, b are arbitrary constants. Its differential equation is _____.

(a)	(1 - x²)y'' + xy' = 0
(b)	(1 - x²)y'' - xy = 0
(c)	(1 - x²)y'' - xy' = 0
(d)	(1 - x²)y'' + xy = 0

104.

The differential equation of family of lines in R² other than vertical lines is _____.

(a)	$x \frac{d y}{d x} = 0$
(b)	$x \frac{d^{2} y}{d x^{2}} = 0$
(c)	$\frac{d y}{d x} = 0$
(d)	$\frac{d^{2} y}{d x^{2}} = 0$

105.

Which of the following differential equation is the solution of the function y = A₁cosx - A₂sinx (where A₁ and A₂ are arbitrary constants) ? (A₁≠ 0, A₂≠ 0)

(a)	y₂ + y₁ = 0
(b)	y₂ - y = 0
(c)	y₂ + y = 0
(d)	y₂ + y₁² = 0

106.

The order and degree of

\frac{d^{2} y}{d x^{2}} + x \cdot 2^{\frac{dy}{dx}} - 3 = 0

are _____ and _____ respectively.

(a)	1, 1
(b)	2, not defined
(c)	Not defined, 1
(d)	2, 1

107.

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)

(a)	xy - x + 1 = 0
(b)	x² - yx + 1 = 0
(c)	x² - y² + 2 = 0
(d)	x + y² + 1 = 0

108.

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

(a)	sinx = c cosy
(b)	cosx • cosy = c
(c)	siny = c cosx
(d)	siny + cosx = c

109.

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 _____.

(a)	$\frac{d v}{1 + v^{2}} = \frac{d x}{x}$
(b)	$\frac{d v}{1 + v^{2}} = x d x$
(c)	$(1 + v^{2}) d v = \frac{1}{x} d x$
(d)	$(1 + v^{2}) d v = x d x$

110.

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

(a)	3
(b)	0
(c)	6
(d)	2

Showing 101 to 110 out of 145 Questions