\[ a y(x)+b x^2+y'(x)^2=0 \] ✓ Mathematica : cpu = 1.28434 (sec), leaf count = 795
\[\left \{\text {Solve}\left [\int _1^x\left (\frac {2 \sqrt {-b K[1]^2-a y(x)} y(x)}{b K[1]^4+a y(x) K[1]^2+4 y(x)^2}+\frac {b K[1]^3+a y(x) K[1]}{b K[1]^4+a y(x) K[1]^2+4 y(x)^2}\right )dK[1]+\int _1^{y(x)}\left (-\frac {\sqrt {-b x^2-a K[2]} x}{b x^4+a K[2] x^2+4 K[2]^2}-\int _1^x\left (\frac {a K[1]}{b K[1]^4+a K[2] K[1]^2+4 K[2]^2}+\frac {2 \sqrt {-b K[1]^2-a K[2]}}{b K[1]^4+a K[2] K[1]^2+4 K[2]^2}-\frac {a K[2]}{\sqrt {-b K[1]^2-a K[2]} \left (b K[1]^4+a K[2] K[1]^2+4 K[2]^2\right )}-\frac {\left (a K[1]^2+8 K[2]\right ) \left (b K[1]^3+a K[2] K[1]\right )}{\left (b K[1]^4+a K[2] K[1]^2+4 K[2]^2\right )^2}-\frac {2 K[2] \left (a K[1]^2+8 K[2]\right ) \sqrt {-b K[1]^2-a K[2]}}{\left (b K[1]^4+a K[2] K[1]^2+4 K[2]^2\right )^2}\right )dK[1]+\frac {2 K[2]}{b x^4+a K[2] x^2+4 K[2]^2}\right )dK[2]=c_1,y(x)\right ],\text {Solve}\left [\int _1^x\left (\frac {b K[3]^3+a y(x) K[3]}{b K[3]^4+a y(x) K[3]^2+4 y(x)^2}-\frac {2 y(x) \sqrt {-b K[3]^2-a y(x)}}{b K[3]^4+a y(x) K[3]^2+4 y(x)^2}\right )dK[3]+\int _1^{y(x)}\left (\frac {\sqrt {-b x^2-a K[4]} x}{b x^4+a K[4] x^2+4 K[4]^2}-\int _1^x\left (\frac {a K[3]}{b K[3]^4+a K[4] K[3]^2+4 K[4]^2}-\frac {2 \sqrt {-b K[3]^2-a K[4]}}{b K[3]^4+a K[4] K[3]^2+4 K[4]^2}+\frac {a K[4]}{\sqrt {-b K[3]^2-a K[4]} \left (b K[3]^4+a K[4] K[3]^2+4 K[4]^2\right )}-\frac {\left (a K[3]^2+8 K[4]\right ) \left (b K[3]^3+a K[4] K[3]\right )}{\left (b K[3]^4+a K[4] K[3]^2+4 K[4]^2\right )^2}+\frac {2 K[4] \left (a K[3]^2+8 K[4]\right ) \sqrt {-b K[3]^2-a K[4]}}{\left (b K[3]^4+a K[4] K[3]^2+4 K[4]^2\right )^2}\right )dK[3]+\frac {2 K[4]}{b x^4+a K[4] x^2+4 K[4]^2}\right )dK[4]=c_1,y(x)\right ]\right \}\] ✗ Maple : cpu = 0. (sec), leaf count = 0
, exception
time expired