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Question Number 30187 by abdo imad last updated on 17/Feb/18

$$solve{xy}^{{}^{\prime }}-2y=x^4.$$

Answered by ajfour last updated on 18/Feb/18

$$\frac{dy}{dx}-\left(\frac{2}{x}\right)y=x^3$$$$e^{-\int \frac{2}{x}dx}=e^{-2\ln x}=\frac{1}{x^2}$$$$\Rightarrow \frac{y}{x^2}=\int xdx+c_1$$$$or\frac{y}{x^2}=\frac{x^2}{2}+c$$$$or\mathit{y}=\frac{{\mathit{x}}^4}{2}+{\mathit{c}\mathit{x}}^2.$$

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