Question

Integrating factor of the differential equation $(x^2+1)\frac{dy}{dx}+2xy=4x^{2}is$

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

Answer 1

Answer: (C)

Diff. equation is $\frac{dy}{dx}+\frac{2x}{x^2+1}y=\frac{4x^2}{x^2+1}$
[Type $\frac{dy}{dx}+Py=Q$]
$I.F.=e^{\int Pdx}=e^{\int \frac{2x}{x^2+1}}$
$=e^{log\left(x^2+1\right)}=x^2+1$.