\[ \left (x^2+y(x)^2\right ) f\left (\frac {y(x)}{\sqrt {x^2+y(x)^2}}\right ) \left (y'(x)^2+1\right )-\left (x y'(x)-y(x)\right )^2=0 \] ✓ Mathematica : cpu = 4.17096 (sec), leaf count = 253
\[\left \{\text {Solve}\left [c_1=\log (x)+\int _1^{\frac {y(x)}{x}} \frac {\left (K[1]^2+1\right ) f\left (\frac {K[1]}{\sqrt {K[1]^2+1}}\right )-1}{(K[1]-i) (K[1]+i) \sqrt {f\left (\frac {K[1]}{\sqrt {K[1]^2+1}}\right )} \left (K[1] \sqrt {f\left (\frac {K[1]}{\sqrt {K[1]^2+1}}\right )}+i \sqrt {f\left (\frac {K[1]}{\sqrt {K[1]^2+1}}\right )-1}\right )} \, dK[1],y(x)\right ],\text {Solve}\left [c_1=\log (x)+\int _1^{\frac {y(x)}{x}} \frac {\left (K[2]^2+1\right ) f\left (\frac {K[2]}{\sqrt {K[2]^2+1}}\right )-1}{(K[2]-i) (K[2]+i) \sqrt {f\left (\frac {K[2]}{\sqrt {K[2]^2+1}}\right )} \left (K[2] \sqrt {f\left (\frac {K[2]}{\sqrt {K[2]^2+1}}\right )}-i \sqrt {f\left (\frac {K[2]}{\sqrt {K[2]^2+1}}\right )-1}\right )} \, dK[2],y(x)\right ]\right \}\]
✓ Maple : cpu = 1.252 (sec), leaf count = 155
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_a}}^{2}+1} \left ( -{\it \_a}\,f \left ( {{\it \_a}{\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}}} \right ) +\sqrt {- \left ( f \left ( {{\it \_a}{\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}}} \right ) \right ) ^{2}+f \left ( {{\it \_a}{\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}}} \right ) } \right ) \left ( f \left ( {{\it \_a}{\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}}} \right ) \right ) ^{-1}}{d{\it \_a}}+{\it \_C1} \right ) x,y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!-{\frac {1}{{{\it \_a}}^{2}+1} \left ( {\it \_a}\,f \left ( {{\it \_a}{\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}}} \right ) +\sqrt {- \left ( f \left ( {{\it \_a}{\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}}} \right ) \right ) ^{2}+f \left ( {{\it \_a}{\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}}} \right ) } \right ) \left ( f \left ( {{\it \_a}{\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}}} \right ) \right ) ^{-1}}{d{\it \_a}}+{\it \_C1} \right ) x \right \} \]