4.7   ODE No. 1007

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

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

Mathematica: cpu = 0.057007 (sec), leaf count = 135 $$\left\{\{y(x)\to c_1{e}^{\sqrt{2}x}+c_2{e}^{-\sqrt{2}x}+\frac{e^{-\sqrt{2}x}(-2e^{x(x+\sqrt{2})}x+2e^{(x-\sqrt{2})x+2\sqrt{2}x}x+\sqrt{2}{e}^{x(x+\sqrt{2})}+\sqrt{2}{e}^{(x-\sqrt{2})x+2\sqrt{2}x})}{2\sqrt{2}}\}\right\}$$

Maple: cpu = 0.016 (sec), leaf count = 26 $$\{y\left(x\right)={\mathrm{e}}^{x\sqrt{2}}\mathit{\_}\mathit{C}\mathit{2}+{\mathrm{e}}^{-x\sqrt{2}}\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{e}}^{x^2}\}$$