General solution of the differential equation $x \cos y \mathrm{~d} y=\left(x \mathrm{e}^x \log x+\mathrm{e}^x\right) \mathrm{d} x$ is (where $C$ is a constant of integration.)

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Aicharya · Accepted Answer

$\begin{aligned} & x \cos y \mathrm{~d} y=\left(x \mathrm{e}^x \log x+\mathrm{e}^xight) \mathrm{d} x \ & \Rightarrow \int \cos y \mathrm{~d} y=\int \mathrm{e}^x\left\{\log x+\frac{1}{x}ight\} \mathrm{d} x \ & \Rightarrow \sin y=\mathrm{e}^x \log x+C\left[\because \int \mathrm{e}^x\left\{f(x)+f^{\prime}(x)ight\} \mathrm{d} x=\mathrm{e}^x f(x)+Cight]\end{aligned}$

General solution of the differential equation $x \cos y \mathrm{~d} y=\left(x \mathrm{e}^x \log…

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