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
$\tan x \cdot \tan y=k$
42
MCQ (Single Correct Answer)
The family $y=A x+A^3$ of curves is represented by differential equation of degree
A
1
B
2
C
3
D
4
43
MCQ (Single Correct Answer)
The integrating factor of $\frac{x d y}{d x}-y=x^4-3 x$ is
A
$x$
B
$\log x$
C
$\frac{1}{x}$
D
$-x$
44
MCQ (Single Correct Answer)
The solution of $\frac{d y}{d x}-y=1, y(0)=1$ is given by
A
$x y=-\mathrm{e}^x$
B
$x y=-\mathrm{e}^{-x}$
C
$x y=-1$
D
$y=2 e^x-1$