4.124   ODE No. 1124

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

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

Mathematica: cpu = 0.063008 (sec), leaf count = 65 $$\left\{\{y(x)\to c_1{}_1{F}_1(-\frac{n}{2};a+\frac{1}{2};x^2)+i^{1-2a}{c}_2{x}^{1-2a}{}_1{F}_1(-a-\frac{n}{2}+\frac{1}{2};\frac{3}{2}-a;x^2)\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 29 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{M}(-\frac{n}{2},\frac{1}{2}+a,x^2)+\mathit{\_}\mathit{C}\mathit{2}\mathit{U}(-\frac{n}{2},\frac{1}{2}+a,x^2)\}$$