5.20   ODE No. 1468

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)-6x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+2(4x^2+2a-1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-8axy\left(x\right)=0}}$$

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

Mathematica: cpu = 0.087011 (sec), leaf count = 57 $$\left\{\{y(x)\to c_2{H}_{\frac{a}{2}}(x){}_1{F}_1(-\frac{a}{4};\frac{1}{2};x^2)+c_1{H}_{\frac{a}{2}}(x){}^2+c_3{}_1{F}_1(-\frac{a}{4};\frac{1}{2};x^2){}^2\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 64 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\left(\mathit{M}(\frac{1}{2}-\frac{a}{4},\frac{3}{2},x^2)\right)}^2{x}^2+\mathit{\_}\mathit{C}\mathit{2}{\left(\mathit{U}(\frac{1}{2}-\frac{a}{4},\frac{3}{2},x^2)\right)}^2{x}^2+\mathit{\_}\mathit{C}\mathit{3}\mathit{M}(\frac{1}{2}-\frac{a}{4},\frac{3}{2},x^2)x^2\mathit{U}(\frac{1}{2}-\frac{a}{4},\frac{3}{2},x^2)\}$$