\[ \left (x^2+y(x)^2\right ) f\left (\frac {x}{\sqrt {x^2+y(x)^2}}\right ) \left (y'(x)^2+1\right )-\left (x y'(x)-y(x)\right )^2=0 \] ✓ Mathematica : cpu = 0.573276 (sec), leaf count = 253
\[\left \{\text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right ) K[1]^2+f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )-1}{\sqrt {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )} (K[1]-i) (K[1]+i) \left (\sqrt {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )} K[1]+i \sqrt {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )-1}\right )}dK[1]=-\log (x)+c_1,y(x)\right ],\text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right ) K[2]^2+f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )-1}{\sqrt {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )} (K[2]-i) (K[2]+i) \left (\sqrt {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )} K[2]-i \sqrt {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )-1}\right )}dK[2]=-\log (x)+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.979 (sec), leaf count = 139
\[\left \{y \left (x \right ) = x \RootOf \left (c_{1}+\int _{}^{\textit {\_Z}}\frac {-\textit {\_a} f \left (\frac {1}{\sqrt {\textit {\_a}^{2}+1}}\right )+\sqrt {-f \left (\frac {1}{\sqrt {\textit {\_a}^{2}+1}}\right )^{2}+f \left (\frac {1}{\sqrt {\textit {\_a}^{2}+1}}\right )}}{\left (\textit {\_a}^{2}+1\right ) f \left (\frac {1}{\sqrt {\textit {\_a}^{2}+1}}\right )}d \textit {\_a} -\ln \left (x \right )\right ), y \left (x \right ) = x \RootOf \left (c_{1}+\int _{}^{\textit {\_Z}}-\frac {\textit {\_a} f \left (\frac {1}{\sqrt {\textit {\_a}^{2}+1}}\right )+\sqrt {-f \left (\frac {1}{\sqrt {\textit {\_a}^{2}+1}}\right )^{2}+f \left (\frac {1}{\sqrt {\textit {\_a}^{2}+1}}\right )}}{\left (\textit {\_a}^{2}+1\right ) f \left (\frac {1}{\sqrt {\textit {\_a}^{2}+1}}\right )}d \textit {\_a} -\ln \left (x \right )\right )\right \}\]