The general solution of the differential equation $x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$ is

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { We have, } x+y \frac{d y}{d x}=\sec \left(x^2+y^2ight) \ & 	ext { Put } x^2+y^2=u \Rightarrow 2 x+2 y \frac{d y}{d x}=\frac{d u}{d x} \ & 	herefore x+y \frac{d y}{d x}=\frac{1}{2} \frac{d u}{d x} \ & 	herefore \frac{1}{2} \frac{d u}{d x}=\sec u \ & 	herefore \int \frac{d u}{\sec u}=\int 2 d x \ & 	herefore \sin u=2 x+c \ & \Rightarrow \sin \left(x^2+y^2ight)=2 x+c\end{aligned}$

The general solution of the differential equation $x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$ is

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