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Question Number 85706 by naka3546 last updated on 24/Mar/20

$$Findthegeneralsolutionof$$$$x^2\sqrt{y^2+9}dx+5\sqrt{x^2-3}ydy=0$$

Answered by mind is power last updated on 24/Mar/20

$$\iff \frac{ydy}{\sqrt{y^2+9}}=-\frac{5\sqrt{x^2-3}}{x^2}$$$$\Rightarrow \sqrt{y^2+9}=5\int -\frac{\sqrt{x^2-3}}{x^2}dx=\frac{\sqrt{x^2-3}}{x}-\int \frac{dx}{\sqrt{x^2-3}}$$$$=\frac{\sqrt{x^2-3}}{x}-argsh\left(\frac{x}{\sqrt{3}}\right)+c$$$$\Rightarrow y={({(\frac{\sqrt{x^2-3}}{x}-argsh\left(\frac{x}{\sqrt{3}}\right)+c)}^2-9)}^{\frac{1}{2}}$$

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