36
MCQ (Single Correct Answer)
The order and degree of the differential equation $\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^{1 / 4}+x^{1 / 5}=0$ respectively, are
A
2 and 4
B
2 and 2
C
2 and 3
D
3 and 3
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
$\sin x$