\[ \text {Global$\grave { }$f}\left (\text {Global$\grave { }$a} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2+\text {Global$\grave { }$x}^2\right ) \left (\text {Global$\grave { }$a} \text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$x}\right )-\text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-\text {Global$\grave { }$y}(\text {Global$\grave { }$x})=0 \] ✓ Mathematica : cpu = 204.295 (sec), leaf count = 88
\[\text {Solve}\left [\int _1^{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})} \left (-\int _1^{\text {Global$\grave { }$x}} \left (1-2 \text {Global$\grave { }$a} K[1] K[2] \text {Global$\grave { }$f}'\left (\text {Global$\grave { }$a} K[2]^2+K[1]^2\right )\right ) \, dK[1]-\text {Global$\grave { }$a} K[2] \text {Global$\grave { }$f}\left (\text {Global$\grave { }$a} K[2]^2+\text {Global$\grave { }$x}^2\right )+\text {Global$\grave { }$x}\right ) \, dK[2]+\int _1^{\text {Global$\grave { }$x}} \left (\text {Global$\grave { }$y}(\text {Global$\grave { }$x})-K[1] \text {Global$\grave { }$f}\left (K[1]^2+\text {Global$\grave { }$a} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2\right )\right ) \, dK[1]=c_1,\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ]\]
✓ Maple : cpu = 0.072 (sec), leaf count = 45
\[ \left \{ -{ax \left ( y \left ( x \right ) \right ) ^{2}{\frac {1}{\sqrt {{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}}-\int ^{-{\frac {a \left ( y \left ( x \right ) \right ) ^{2}}{2}}-{\frac {{x}^{2}}{2}}}\!f \left ( -2\,{\it \_a} \right ) {d{\it \_a}}+{\it \_C1}=0 \right \} \]