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Question Number 183038 by Mastermind last updated on 18/Dec/22

$$\mathrm{Solve}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{xy}={\mathrm{x}}^2$$$$$$$$\mathrm{M}.\mathrm{m}$$

Answered by TheSupreme last updated on 21/Dec/22

$$D\left({ye}^{\frac{x^2}{2}}\right)=x^2{e}^{\frac{x^2}{2}}$$$$y{e}^{\frac{x^2}{2}}=\int x^2{e}^{\frac{x^2}{2}}dx=\frac{1}{2}{xe}^{\frac{x^2}{2}}-\frac{1}{2}\int e^{\frac{x^2}{2}}dx$$$$y=\frac{1}{2}x-\frac{1}{2}\sqrt{\pi }erfi\left(x\right)e^{-\frac{x^2}{2}}+c$$$$$$

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