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73
MCQ (Single Correct Answer)

The solution of differential equation $\frac{d y}{d x}=e^{x-y}+x^2 e^{-y}$ is

A
$y=e^{x-y}-x^2 \mathrm{e}^{-y}+C$
B
$\mathrm{e}^y-\mathrm{e}^x=\frac{x^3}{3}+\mathrm{C}$
C
$\mathrm{e}^x+\mathrm{e}^y=\frac{x^3}{3}+\mathrm{C}$
D
$\mathrm{e}^x-\mathrm{e}^y=\frac{x^3}{3}+C$
74
MCQ (Single Correct Answer)

The solution of differential equation $\frac{d y}{d x}+\frac{2 x y}{1+x^2}=\frac{1}{\left(1+x^2\right)^2}$ is

A
$y\left(1+x^2\right)=C+\tan ^{-1} x$
B
$\frac{y}{1+x^2}=C+\tan ^{-1} x$
C
$y \log \left(1+x^2\right)=C+\tan ^{-1} x$
D
$y\left(1+x^2\right)=C+\sin ^{-1} x$
75

The degree of the differential equation $\frac{d^2 y}{d x^2}+e^{d y / d x}=0$ is ............ .

Explanation

Given differential equation is

$$\frac{d^2 y}{d x^2}+e^{\frac{d y}{d x}}=0$$

Degree of this equation is not defined.

76

The degree of the differential equation $\sqrt{1+\left(\frac{d y}{d x}\right)^2}=x$ is ................. .

Explanation

Given differential equation is $\sqrt{1+\left(\frac{d y}{d x}\right)^2}=x$

So, degree of this equation is two.

77

The number of arbitrary constants in the general solution of a differential equation of order three is .......... .

Explanation

There are three arbitrary constants.