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
$3,2$
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
$2 x \frac{d y}{d x}+y\left(\frac{d y}{d x}\right)^2-y=0$