Question

An integrating factor of the differential equation
$(1-x^2)\frac{dy}{dx}+xy=\frac{x^4}{(1+x^5)}(\sqrt{1-x^2}{)}^3$ is:

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

Answer 1

Answer: (D)

$\frac{1}{\sqrt{1-x^2}}$

I.F = $e^{\int \frac{x}{1-x^2}dx}$

Put $1-x^2=t$

$\Rightarrow -2xdx=dt$

$I.F.=e^{\frac{-1}{2}\int \frac{1}{t}dt}$

$=e^{\frac{-1}{2}lnt}$

$=\frac{1}{\sqrt{t}}$

$=\frac{1}{\sqrt{1-x^2}}$