3.326   ODE No. 326

$$\boxed{{\displaystyle y\left(x\right)({(ay\left(x\right)+bx)}^3+b{x}^3)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+x({(ay\left(x\right)+bx)}^3+a{\left(y\left(x\right)\right)}^3)=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.272035 (sec), leaf count = 13289 $$\{\{y(x)\to -\frac{bx}{2a}-\frac{1}{2}\sqrt{\frac{b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}+\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}+\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}+\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}}-\frac{1}{2}\sqrt{\frac{2b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}-\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}-\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}-\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}-\frac{-\frac{8b^3{x}^3}{a^3}-\frac{16b(x^2-e^{2c_1})x}{a}-\frac{8b(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2)x}{a^3}}{4\sqrt{\frac{b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}+\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}+\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}+\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}}}}\},\{y(x)\to -\frac{bx}{2a}-\frac{1}{2}\sqrt{\frac{b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}+\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}+\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}+\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}}+\frac{1}{2}\sqrt{\frac{2b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}-\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}-\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}-\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}-\frac{-\frac{8b^3{x}^3}{a^3}-\frac{16b(x^2-e^{2c_1})x}{a}-\frac{8b(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2)x}{a^3}}{4\sqrt{\frac{b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}+\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}+\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}+\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}}}}\},\{y(x)\to -\frac{bx}{2a}+\frac{1}{2}\sqrt{\frac{b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}+\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}+\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}+\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}}-\frac{1}{2}\sqrt{\frac{2b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}-\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}-\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}-\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}+\frac{-\frac{8b^3{x}^3}{a^3}-\frac{16b(x^2-e^{2c_1})x}{a}-\frac{8b(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2)x}{a^3}}{4\sqrt{\frac{b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}+\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}+\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}+\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}}}}\},\{y(x)\to -\frac{bx}{2a}+\frac{1}{2}\sqrt{\frac{b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}+\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}+\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}+\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}}+\frac{1}{2}\sqrt{\frac{2b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}-\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}-\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}-\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}+\frac{-\frac{8b^3{x}^3}{a^3}-\frac{16b(x^2-e^{2c_1})x}{a}-\frac{8b(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2)x}{a^3}}{4\sqrt{\frac{b^2{x}^2}{a^2}+\frac{e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2}{a^2}+\frac{-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2}{3a^2}+\frac{\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}{3\sqrt[3]{2}{a}^2}+\frac{\sqrt[3]{2}(e^{2c_1}{a}^2-x^2{a}^2-b^2{x}^2-x^2){}^2}{3a^2\sqrt[3]{108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3+\sqrt{(108b^2{x}^2(x^2-e^{2c_1}){}^2{a}^4-108b^4{x}^4(e^{2c_1}-x^2)a^2+72b^2{x}^2(e^{2c_1}-x^2)(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2-36b^2{x}^2(x^2-e^{2c_1})(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2)a^2+2(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^3){}^2-4(-12a^2{b}^2(e^{2c_1}-x^2)x^2-12a^2{b}^2(x^2-e^{2c_1})x^2+(-e^{2c_1}{a}^2+x^2{a}^2+b^2{x}^2+x^2){}^2){}^3}}}}}}\}\}$$

Maple: cpu = 0.343 (sec), leaf count = 160 $$\{y\left(x\right)=\frac{x(\mathit{\_}\mathit{C}\mathit{1}x-b\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(b^2{\mathit{\_}\mathit{Z}}^4-2bx\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^3+(a^2{x}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+b^2{x}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-a^2){\mathit{\_}\mathit{Z}}^2-2b{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3\mathit{\_}\mathit{Z}+x^4{\mathit{\_}\mathit{C}\mathit{1}}^4))}{a\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(b^2{\mathit{\_}\mathit{Z}}^4-2bx\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^3+(a^2{x}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+b^2{x}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-a^2){\mathit{\_}\mathit{Z}}^2-2b{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3\mathit{\_}\mathit{Z}+x^4{\mathit{\_}\mathit{C}\mathit{1}}^4)}\}$$