67
MCQ (Single Correct Answer)
The order and degree of differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]=\frac{d^2 y}{d x^2}$ are
A
$2, \frac{3}{2}$
B
$2, 3$
C
$2,1$
D
$3,4$
68
MCQ (Single Correct Answer)
The differential equation of family of curves $y^2=4 a(x+a)$ is
A
$y^2=4 \frac{d y}{d x}\left(x+\frac{d y}{d x}\right)$
B
$2 y \frac{d y}{d x}=4 a$
C
$y \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0$
D
$2 x \frac{d y}{d x}+y\left(\frac{d y}{d x}\right)^2-y=0$
69
MCQ (Single Correct Answer)
Which of the following is the general solution of $\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+y=0$ ?
A
$y=(A x+B) e^x$
B
$y=(A x+B) \mathrm{e}^{-x}$
C
$y=A e^x+B e^{-x}$
D
$y=A \cos x+B \sin x$
70
MCQ (Single Correct Answer)
The general solution of $\frac{d y}{d x}+y \tan x=\sec x$ is
A
$y \sec x=\tan x+C$
B
$y \tan x=\sec x+C$
C
$\tan x=y \tan x+C$
D
$x \sec x=\tan y+C$
71
MCQ (Single Correct Answer)
The solution of differential equation $\frac{d y}{d x}+\frac{y}{x}=\sin x$ is
A
$x(y+\cos x)=\sin x+C$
B
$x(y-\cos x)=\sin x+C$
C
$x y \cos x=\sin x+C$
D
$x(y+\cos x)=\cos x+C$