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Exercise

$\frac{dy}{dx}=\left(\frac{x}{y}\right)\left(\frac{\sqrt{1+y^2}}{\sqrt{1+x^2}}\right)^{\frac{1}{2}}$

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Final answer to the exercise

$y=\sqrt{\sqrt[3]{\left(\sqrt[4]{\left(1+x^2\right)^{3}}+C_2\right)^{4}}-1},\:y=-\sqrt{\sqrt[3]{\left(\sqrt[4]{\left(1+x^2\right)^{3}}+C_2\right)^{4}}-1}$

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