\[ y(x) y'(x) \left ((a y(x)+b x)^3+b x^3\right )+x \left ((a y(x)+b x)^3+a y(x)^3\right )=0 \] ✓ Mathematica : cpu = 4.86889 (sec), leaf count = 6861
\[\left \{\left \{y(x)\to -\frac {\sqrt {3} \sqrt {\frac {\left (x^2-e^{2 c_1}\right ) a^2+3 b^2 x^2+\left (b^2+1\right ) x^2+3 \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {\left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^2}} a+\sqrt {3} \sqrt {-\frac {-6 a b^2 x^2+\frac {6 \sqrt {3} b \left (\left (e^{2 c_1}-x^2\right ) a^2+x^2\right ) x}{\sqrt {\frac {\left (x^2-e^{2 c_1}\right ) a^2+3 b^2 x^2+\left (b^2+1\right ) x^2+3 \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {\left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^2}}}-4 a \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+a \sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {a \left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^3}} a+3 b x}{6 a}\right \},\left \{y(x)\to \frac {-\sqrt {3} \sqrt {\frac {\left (x^2-e^{2 c_1}\right ) a^2+3 b^2 x^2+\left (b^2+1\right ) x^2+3 \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {\left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^2}} a+\sqrt {3} \sqrt {-\frac {-6 a b^2 x^2+\frac {6 \sqrt {3} b \left (\left (e^{2 c_1}-x^2\right ) a^2+x^2\right ) x}{\sqrt {\frac {\left (x^2-e^{2 c_1}\right ) a^2+3 b^2 x^2+\left (b^2+1\right ) x^2+3 \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {\left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^2}}}-4 a \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+a \sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {a \left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^3}} a-3 b x}{6 a}\right \},\left \{y(x)\to \frac {\sqrt {3} \sqrt {\frac {\left (x^2-e^{2 c_1}\right ) a^2+3 b^2 x^2+\left (b^2+1\right ) x^2+3 \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {\left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^2}} a-\sqrt {3} \sqrt {\frac {6 a b^2 x^2+\frac {6 \sqrt {3} b \left (\left (e^{2 c_1}-x^2\right ) a^2+x^2\right ) x}{\sqrt {\frac {\left (x^2-e^{2 c_1}\right ) a^2+3 b^2 x^2+\left (b^2+1\right ) x^2+3 \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {\left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^2}}}+4 a \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )-a \sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}-\frac {a \left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^3}} a-3 b x}{6 a}\right \},\left \{y(x)\to \frac {\sqrt {3} \sqrt {\frac {\left (x^2-e^{2 c_1}\right ) a^2+3 b^2 x^2+\left (b^2+1\right ) x^2+3 \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {\left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^2}} a+\sqrt {3} \sqrt {\frac {6 a b^2 x^2+\frac {6 \sqrt {3} b \left (\left (e^{2 c_1}-x^2\right ) a^2+x^2\right ) x}{\sqrt {\frac {\left (x^2-e^{2 c_1}\right ) a^2+3 b^2 x^2+\left (b^2+1\right ) x^2+3 \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )+\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}+\frac {\left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^2}}}+4 a \left (a^2 \left (e^{2 c_1}-x^2\right )-\left (b^2+1\right ) x^2\right )-a \sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}-\frac {a \left (\left (x^2-e^{2 c_1}\right ) a^2+\left (b^2+1\right ) x^2\right ){}^2}{\sqrt [3]{-\left (e^{2 c_1}-x^2\right ){}^3 a^6+3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4-3 \left (b^4-16 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2+b^6 x^6+3 b^4 x^6+3 b^2 x^6+x^6+6 \sqrt {3} \sqrt {-a^2 b^2 x^4 \left (e^{2 c_1}-x^2\right ) \left (\left (e^{2 c_1}-x^2\right ){}^3 a^6-3 \left (b^2+1\right ) x^2 \left (e^{2 c_1}-x^2\right ){}^2 a^4+3 \left (b^4-7 b^2+1\right ) x^4 \left (e^{2 c_1}-x^2\right ) a^2-\left (b^2+1\right )^3 x^6\right )}}}}{a^3}} a-3 b x}{6 a}\right \}\right \}\]
✓ Maple : cpu = 0.494 (sec), leaf count = 160
\[ \left \{ y \left ( x \right ) ={\frac {x \left ( {\it \_C1}\,x-b{\it RootOf} \left ( {b}^{2}{{\it \_Z}}^{4}-2\,bx{\it \_C1}\,{{\it \_Z}}^{3}+ \left ( {a}^{2}{x}^{2}{{\it \_C1}}^{2}+{b}^{2}{x}^{2}{{\it \_C1}}^{2}+{{\it \_C1}}^{2}{x}^{2}-{a}^{2} \right ) {{\it \_Z}}^{2}-2\,b{x}^{3}{{\it \_C1}}^{3}{\it \_Z}+{x}^{4}{{\it \_C1}}^{4} \right ) \right ) }{a{\it RootOf} \left ( {b}^{2}{{\it \_Z}}^{4}-2\,bx{\it \_C1}\,{{\it \_Z}}^{3}+ \left ( {a}^{2}{x}^{2}{{\it \_C1}}^{2}+{b}^{2}{x}^{2}{{\it \_C1}}^{2}+{{\it \_C1}}^{2}{x}^{2}-{a}^{2} \right ) {{\it \_Z}}^{2}-2\,b{x}^{3}{{\it \_C1}}^{3}{\it \_Z}+{x}^{4}{{\it \_C1}}^{4} \right ) }} \right \} \]