4.48   ODE No. 1048

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-4x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(3x^2+2n-1)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.010001 (sec), leaf count = 45 $$\left\{\{y(x)\to c_1{e}^{\frac{x^2}{2}}{H}_n(x)+c_2{e}^{\frac{x^2}{2}}{}_1{F}_1(-\frac{n}{2};\frac{1}{2};x^2)\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 43 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{x^2}{2}}\mathit{M}(-\frac{n}{2}+\frac{1}{2},\frac{3}{2},x^2)x+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{x^2}{2}}\mathit{U}(-\frac{n}{2}+\frac{1}{2},\frac{3}{2},x^2)x\}$$