\[ y(x) y'(x) \left ((a y(x)+b x)^3+b x^3\right )+x \left ((a y(x)+b x)^3+a y(x)^3\right )=0 \] ✓ Mathematica : cpu = 4.93203 (sec), leaf count = 13289
\[\left \{\left \{y(x)\to -\frac {b x}{2 a}-\frac {1}{2} \sqrt {\frac {b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}+\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}+\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}+\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}}-\frac {1}{2} \sqrt {\frac {2 b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}-\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}-\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}-\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}-\frac {-\frac {8 b^3 x^3}{a^3}-\frac {16 b \left (x^2-e^{2 c_1}\right ) x}{a}-\frac {8 b \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ) x}{a^3}}{4 \sqrt {\frac {b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}+\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}+\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}+\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}}}}\right \},\left \{y(x)\to -\frac {b x}{2 a}-\frac {1}{2} \sqrt {\frac {b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}+\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}+\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}+\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}}+\frac {1}{2} \sqrt {\frac {2 b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}-\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}-\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}-\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}-\frac {-\frac {8 b^3 x^3}{a^3}-\frac {16 b \left (x^2-e^{2 c_1}\right ) x}{a}-\frac {8 b \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ) x}{a^3}}{4 \sqrt {\frac {b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}+\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}+\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}+\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}}}}\right \},\left \{y(x)\to -\frac {b x}{2 a}+\frac {1}{2} \sqrt {\frac {b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}+\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}+\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}+\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}}-\frac {1}{2} \sqrt {\frac {2 b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}-\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}-\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}-\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}+\frac {-\frac {8 b^3 x^3}{a^3}-\frac {16 b \left (x^2-e^{2 c_1}\right ) x}{a}-\frac {8 b \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ) x}{a^3}}{4 \sqrt {\frac {b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}+\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}+\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}+\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}}}}\right \},\left \{y(x)\to -\frac {b x}{2 a}+\frac {1}{2} \sqrt {\frac {b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}+\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}+\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}+\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}}+\frac {1}{2} \sqrt {\frac {2 b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}-\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}-\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}-\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}+\frac {-\frac {8 b^3 x^3}{a^3}-\frac {16 b \left (x^2-e^{2 c_1}\right ) x}{a}-\frac {8 b \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ) x}{a^3}}{4 \sqrt {\frac {b^2 x^2}{a^2}+\frac {e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2}{a^2}+\frac {-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2}{3 a^2}+\frac {\sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}{3 \sqrt [3]{2} a^2}+\frac {\sqrt [3]{2} \left (e^{2 c_1} a^2-x^2 a^2-b^2 x^2-x^2\right ){}^2}{3 a^2 \sqrt [3]{108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3+\sqrt {\left (108 b^2 x^2 \left (x^2-e^{2 c_1}\right ){}^2 a^4-108 b^4 x^4 \left (e^{2 c_1}-x^2\right ) a^2+72 b^2 x^2 \left (e^{2 c_1}-x^2\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2-36 b^2 x^2 \left (x^2-e^{2 c_1}\right ) \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ) a^2+2 \left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^3\right ){}^2-4 \left (-12 a^2 b^2 \left (e^{2 c_1}-x^2\right ) x^2-12 a^2 b^2 \left (x^2-e^{2 c_1}\right ) x^2+\left (-e^{2 c_1} a^2+x^2 a^2+b^2 x^2+x^2\right ){}^2\right ){}^3}}}}}}\right \}\right \}\]
✓ Maple : cpu = 0.494 (sec), leaf count = 160
\[ \left \{ y \left ( x \right ) ={\frac {x \left ( {\it \_C1}\,x-b{\it RootOf} \left ( {b}^{2}{{\it \_Z}}^{4}-2\,bx{\it \_C1}\,{{\it \_Z}}^{3}+ \left ( {a}^{2}{x}^{2}{{\it \_C1}}^{2}+{b}^{2}{x}^{2}{{\it \_C1}}^{2}+{{\it \_C1}}^{2}{x}^{2}-{a}^{2} \right ) {{\it \_Z}}^{2}-2\,b{x}^{3}{{\it \_C1}}^{3}{\it \_Z}+{x}^{4}{{\it \_C1}}^{4} \right ) \right ) }{a{\it RootOf} \left ( {b}^{2}{{\it \_Z}}^{4}-2\,bx{\it \_C1}\,{{\it \_Z}}^{3}+ \left ( {a}^{2}{x}^{2}{{\it \_C1}}^{2}+{b}^{2}{x}^{2}{{\it \_C1}}^{2}+{{\it \_C1}}^{2}{x}^{2}-{a}^{2} \right ) {{\it \_Z}}^{2}-2\,b{x}^{3}{{\it \_C1}}^{3}{\it \_Z}+{x}^{4}{{\it \_C1}}^{4} \right ) }} \right \} \]