4.280   ODE No. 1280

$$\boxed{{\displaystyle 4x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+8x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-(4x^2+12x+3)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.039005 (sec), leaf count = 52 $$\left\{\{y(x)\to \frac{c_2{e}^{-x}(4e^{2x}{x}^2\text{Ei}(-2x)+2x-1)}{2x^{3/2}}+c_1{e}^x\sqrt{x}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 41 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{x}{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{2}(4x^2{\mathrm{e}}^x\mathit{E}\mathit{i}(1,2x)-2{\mathrm{e}}^{-x}x+{\mathrm{e}}^{-x})x^{-\frac{3}{2}}\}$$