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Question Number 30188 by abdo imad last updated on 17/Feb/18

$$solve{x}^3(x^2+1)y^{{}^{\prime }}-2xy=0$$

Commented by mrW2 last updated on 17/Feb/18

$$x^3(x^2+1)y^{{}^{\prime }}-2xy=0$$$$x^2(x^2+1)y^{{}^{\prime }}=2y$$$$\frac{dy}{y}=\frac{2dx}{x^2(x^2+1)}$$$$\int \frac{dy}{y}=2\int (\frac{1}{x^2}-\frac{1}{x^2+1})dx$$$$\ln y=-2(\frac{1}{x}+{\tan }^{-1}x)+C_1$$$$\Rightarrow y={ce}^{-2(\frac{1}{x}+{\tan }^{-1}x)}$$

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