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Question-128254




Question Number 128254 by Ahmed1hamouda last updated on 05/Jan/21
Answered by mr W last updated on 06/Jan/21
(dy/dx)+2xy=xe^(−x)   IF=e^(∫2xdx) =e^x^2    y=((∫e^x^2  xe^(−x) dx+C)/e^x^2  )  y=e^(−x^2 ) (∫e^(x^2 −x) xdx+C)
$$\frac{{dy}}{{dx}}+\mathrm{2}{xy}={xe}^{−{x}} \\ $$$${IF}={e}^{\int\mathrm{2}{xdx}} ={e}^{{x}^{\mathrm{2}} } \\ $$$${y}=\frac{\int{e}^{{x}^{\mathrm{2}} } {xe}^{−{x}} {dx}+{C}}{{e}^{{x}^{\mathrm{2}} } } \\ $$$${y}={e}^{−{x}^{\mathrm{2}} } \left(\int{e}^{{x}^{\mathrm{2}} −{x}} {xdx}+{C}\right) \\ $$

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