37
MCQ (Single Correct Answer)
If $y=e^{-x}(A \cos x+B \sin x)$, then $y$ is a solution of
A
$\frac{d^2 y}{d x^2}+2 \frac{d y}{d x}=0$
B
$\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+2 y=0$
C
$\frac{d^2 y}{d x^2}+2 \frac{d y}{d x}+2 y=0$
D
$\frac{d^2 y}{d x^2}+2 y=0$
38
MCQ (Single Correct Answer)
The differential equation for $y=A \cos \alpha x+B \sin \alpha x$, where $A$ and $B$ are arbitrary constants is
A
$\frac{d^2 y}{d x^2}-\alpha^2 y=0$
B
$\frac{d^2 y}{d x^2}+\alpha^2 y=0$
C
$\frac{d^2 y}{d x^2}+\alpha y=0$
D
$\frac{d^2 y}{d x^2}-\alpha y=0$
39
MCQ (Single Correct Answer)
The solution of differential equation $x d y-y d x=0$ represents
A
a rectangular hyperbola
B
parabola whose vertex is at origin
C
straight line passing through origin
D
a circle whose centre is at origin
40
MCQ (Single Correct Answer)
The integrating factor of differential equation $\cos x \frac{d y}{d x}+y \sin x=1$ is
A
$\cos x$
B
$\tan x$
C
$\sec x$
D
$\sin x$
41
MCQ (Single Correct Answer)
The solution of differential equation $\tan y \sec ^2 x d x+\tan x \sec ^2 y d y=0$ is
A
$\tan x+\tan y=k$
B
$\tan x-\tan y=k$
C
$\frac{\tan x}{\tan y}=k$
D
$\tan x \cdot \tan y=k$