62
MCQ (Single Correct Answer)
The general solution of differential equation $\frac{d y}{d x}=e^{\frac{x^2}{2}}+x y$ is
A
$y=C e^{-x^2 / 2}$
B
$y=C e^{x^2 / 2}$
C
$y=(x+C) e^{x^{2 / 2}}$
D
$y=(C-x) e^{x^2 / 2}$
63
MCQ (Single Correct Answer)
The solution of equation $(2 y-1) d x-(2 x+3) d y=0$ is
A
$\frac{2 x-1}{2 y+3}=k$
B
$\frac{2 y+1}{2 x-3}=k$
C
$\frac{2 x+3}{2 y-1}=k$
D
$\frac{2 x-1}{2 y-1}=k$
64
MCQ (Single Correct Answer)
The differential equation for which $y=a \cos x+b \sin x$ is a solution, is
A
$\frac{d^2 y}{d x^2}+y=0$
B
$\frac{d^2 y}{d x^2}-y=0$
C
$\frac{d^2 y}{d x^2}+(a+b) y=0$
D
$\frac{d^2 y}{d x^2}+(a-b) y=0$
65
MCQ (Single Correct Answer)
The solution of $\frac{d y}{d x}+y=e^{-x}, y(0)=0$ is
A
$y=\mathrm{e}^{-x}(x-1)$
B
$y=x e^x$
C
$y=x \mathrm{e}^{-x}+1$
D
$y=x e^{-x}$
66
MCQ (Single Correct Answer)
The order and degree of differential equation
$$\left(\frac{d^3 y}{d x^3}\right)^2-3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^4 \text { are }$$
A
$1, 4$
B
$3, 4$
C
$2,4$
D
$3,2$