\[ \left (x^2+y(x)^2\right ) f\left (\frac {x}{\sqrt {x^2+y(x)^2}}\right ) \left (y'(x)^2+1\right )-\left (x y'(x)-y(x)\right )^2=0 \] ✓ Mathematica : cpu = 4.34688 (sec), leaf count = 251
\[\left \{\text {Solve}\left [\int _1^{\frac {y(x)}{x}} \frac {K[1]^2 f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )+f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )-1}{(K[1]-i) (K[1]+i) \sqrt {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )} \left (K[1] \sqrt {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )}+i \sqrt {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )-1}\right )} \, dK[1]=c_1-\log (x),y(x)\right ],\text {Solve}\left [\int _1^{\frac {y(x)}{x}} \frac {K[2]^2 f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )+f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )-1}{(K[2]-i) (K[2]+i) \sqrt {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )} \left (K[2] \sqrt {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )}-i \sqrt {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )-1}\right )} \, dK[2]=c_1-\log (x),y(x)\right ]\right \}\] ✓ Maple : cpu = 1.271 (sec), leaf count = 139
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac {1}{{{\it \_a}}^{2}+1} \left ( -{\it \_a}\,f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) +\sqrt {- \left ( f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) \right ) ^{2}+f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) } \right ) \left ( f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) \right ) ^{-1}}{d{\it \_a}}+{\it \_C1} \right ) x,y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!-{\frac {1}{{{\it \_a}}^{2}+1} \left ( {\it \_a}\,f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) +\sqrt {- \left ( f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) \right ) ^{2}+f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) } \right ) \left ( f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) \right ) ^{-1}}{d{\it \_a}}+{\it \_C1} \right ) x \right \} \]