4.123   ODE No. 1123

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

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

Mathematica: cpu = 0.012002 (sec), leaf count = 91 $$\left\{\{y(x)\to c_1{e}^{\frac{1}{2}\sqrt{b}{x}^2(\frac{a}{\sqrt{b}}-\frac{\sqrt{a^2-b}}{\sqrt{b}})}+c_2{e}^{\frac{1}{2}\sqrt{b}{x}^2(\frac{\sqrt{a^2-b}}{\sqrt{b}}+\frac{a}{\sqrt{b}})}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 45 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{x^2}{2}(\sqrt{a^2-b}+a)}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{x^2}{2}(\sqrt{a^2-b}-a)}\}$$