4.54   ODE No. 1054

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

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

Mathematica: cpu = 0.048006 (sec), leaf count = 172 $$\left\{\{y(x)\to c_1{e}^{\frac{cx}{a}-\frac{a{x}^2}{2}-bx}{H}_{\frac{-a^3+a^{2}d-abc+c^2}{a^3}}(\frac{ab-2c}{\sqrt{2}{a}^{3/2}}+\frac{\sqrt{a}x}{\sqrt{2}})+c_2{e}^{\frac{cx}{a}-\frac{a{x}^2}{2}-bx}{}_1{F}_1(-\frac{-a^3+d{a}^2-bca+c^2}{2a^3};\frac{1}{2};{(\frac{ab-2c}{\sqrt{2}{a}^{3/2}}+\frac{\sqrt{a}x}{\sqrt{2}})}^2)\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 105 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{cx}{a}}\mathit{M}(\frac{d{a}^2-abc+c^2}{2a^3},\frac{1}{2},-\frac{{(a^{2}x+ab-2c)}^2}{2a^3})+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{cx}{a}}\mathit{U}(\frac{d{a}^2-abc+c^2}{2a^3},\frac{1}{2},-\frac{{(a^{2}x+ab-2c)}^2}{2a^3})\}$$