4.153   ODE No. 1153

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

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

Mathematica: cpu = 0.033504 (sec), leaf count = 56 $$\left\{\{y(x)\to c_1\sqrt{x}{J}_{\frac{1}{2}(2v-1)}\left(\sqrt{a}x\right)+c_2\sqrt{x}{Y}_{\frac{1}{2}(2v-1)}\left(\sqrt{a}x\right)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 33 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{x}{\mathit{J}}_{v-\frac{1}{2}}\left(\sqrt{a}x\right)+\mathit{\_}\mathit{C}\mathit{2}\sqrt{x}{\mathit{Y}}_{v-\frac{1}{2}}\left(\sqrt{a}x\right)\}$$