Question

I.F. of $(1+x^2)\frac{dy}{dx}+2xy=4x^2$ is:

• A. $2x$
• B. $\frac{1}{1+x^2}$
• C. $1+x^2$
• D. $x^2$

Answer 1

The correct option is C $1+x^2$

$y^1+\frac{2x}{1+x^2}y=4x{}^2$

$I.F=e^{\int P\left(n\right)dx}=e^{\int \frac{2xdx}{1+x^2}}$

$t=1+x^2$

$dt=2xdx$

$\Rightarrow e^{\int \frac{dt}{t}}=e^{logt}=t$

$\Rightarrow I.F=(1+x^2)$