The integrating factor of differential equation $\left(1+y+x^{2} y\right) d x+\left(x+x^{3}\right) d y=0$ is

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Aicharya · Accepted Answer

We have $\left(1+y+x^{2} yight) d x+\left(x+x^{3}ight) d y=0$ $	herefore \frac{d y}{d x}=\frac{-\left(1+y+x^{2} yight)}{x\left(1+x^{2}ight)}=\frac{-\left[1+y\left(1+x^{2}ight)ight]}{x\left(1+x^{2}ight)}$ $	herefore \frac{d y}{d x}=\frac{-1}{x\left(1+x^{2}ight)}-\frac{y\left(1+x^{2}ight)}{x\left(1+x^{2}ight)}$ $	herefore \frac{d y}{d x}+\left(\frac{1}{x}ight) y=\frac{-1}{x\left(1+x^{2}ight)}$ $	herefore$ I.F. $=e^{\int \frac{1}{x} d x}=e^{\log x}=x$

The integrating factor of differential equation $\left(1+y+x^{2} y\right) d x+\left(x+x^{3}\right) d y=0$ is

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