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Question Number 93059 by Ar Brandon last updated on 10/May/20

$${\mathrm{y}}^{{}^{\prime }}+2\mathrm{xy}=\cos \mathrm{x}+2\mathrm{x}\sin \mathrm{x}$$

Answered by TANMAY PANACEA ... last updated on 10/May/20

$$dy+2xydx=cosxdx+2xsinxdx$$$$d\left(y\right)+yd\left(x^2\right)=d\left(sinx\right)+sinxd\left(x^2\right)$$$$d\left(y\right)-d\left(sinx\right)=sinxd\left(x^2\right)-yd\left(x^2\right)$$$$d(y-sinx)=-d\left(x^2\right)(y-sinx)$$$$\frac{d(y-sinx)}{y-sinx}+d\left(x^2\right)=dc$$$$\int \frac{d(y-sinx)}{y-sinx}+\int d\left(x^2\right)=\int dc$$$$ln(y-sinx)+x^2=c$$

Commented by Ar Brandon last updated on 10/May/20

Thanks ��

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