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Question Number 27032 by cmaxamuud98 @gmail.com last updated on 01/Jan/18

$$xy=(1-x^2)\frac{dy}{dx}x=0y=1$$

Commented by abdo imad last updated on 01/Jan/18

$$e.d\Rightarrow (1-x^2)y^{{}^{\prime }}-xy=0withy\left(0\right)=1$$$$\Rightarrow \frac{y^{{}^{\prime }}}{y}=\frac{x}{1-x^2}\Rightarrow ln/y/=\int \frac{xdx}{1-x^2}+\lambda$$$$ln/y/=-\frac{1}{2}ln/1-x^2/+\lambda$$$$\Rightarrow y\left(x\right)=k{e}^{-\frac{1}{2}ln/1-x^{2/}}$$$$\Rightarrow y\left(x\right)=\frac{k}{\sqrt{/1-x^2/}}$$$$y\left(0\right)=1\Rightarrow k=1soy\left(x\right)=\frac{1}{\sqrt{/1-x^2/}}.$$

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