4.170   ODE No. 1170

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

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

Mathematica: cpu = 0.022503 (sec), leaf count = 58 $$\left\{\{y(x)\to c_1{j}_{\frac{1}{2}(\sqrt{1-4b}-1)}\left(\sqrt{a}x\right)+c_2{y}_{\frac{1}{2}(\sqrt{1-4b}-1)}\left(\sqrt{a}x\right)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 45 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{\frac{1}{2}\sqrt{1-4b}}\left(\sqrt{a}x\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_{\frac{1}{2}\sqrt{1-4b}}\left(\sqrt{a}x\right)\frac{1}{\sqrt{x}}\}$$