4.315   ODE No. 1315

$$\boxed{{\displaystyle x(x^2-1)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right)a{x}^3=0}}$$

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

Mathematica: cpu = 0.027503 (sec), leaf count = 44 $$\left\{\{y(x)\to c_2\sin \left(\sqrt{a}\sqrt{x^2-1}\right)+c_1\cos \left(\sqrt{a}\sqrt{x^2-1}\right)\}\right\}$$

Maple: cpu = 0.015 (sec), leaf count = 45 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sin \left((1+x)(x-1)\sqrt{a}\frac{1}{\sqrt{x^2-1}}\right)+\mathit{\_}\mathit{C}\mathit{2}\cos \left((1+x)(x-1)\sqrt{a}\frac{1}{\sqrt{x^2-1}}\right)\}$$