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  4. Integrating factor of the differential equation (x2+1)(dy/dx)+2xy=4x2 is

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

Differential Equations

Solution:

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