2.1049   ODE No. 1049

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

$$(4x^2-1)y(x)+y^{″}(x)-4x{y}^{\prime }(x)-e^x=0$$ ✓ Mathematica : cpu = 0.0596761 (sec), leaf count = 109

$$\left\{\{y(x)\to c_1{e}^{x(x-i)}-\frac{1}{2}i{c}_2{e}^{(x-i)x+2ix}+\frac{1}{4}\sqrt{\pi }{e}^{x(x-i)-\frac{i}{2}}(e^{2ix}\text{erfi}((\frac{1}{2}+\frac{i}{2})-ix)-i{e}^i\text{erf}(-x+(\frac{1}{2}+\frac{i}{2})))\}\right\}$$

✓ Maple : cpu = 0.157 (sec), leaf count = 70

$$\{y\left(x\right)={\mathrm{e}}^{x^2}\cos \left(x\right)\mathit{\_}\mathit{C}\mathit{2}+{\mathrm{e}}^{x^2}\sin \left(x\right)\mathit{\_}\mathit{C}\mathit{1}-\frac{{\mathrm{e}}^{x^2}\sqrt{\pi }(-(i\cos \left(x\right)+\sin \left(x\right)){\mathrm{e}}^{\frac{i}{2}}\mathit{E}\mathit{r}\mathit{f}(x-\frac{1}{2}-\frac{i}{2})+{\mathrm{e}}^{-\frac{i}{2}}(i\cos \left(x\right)-\sin \left(x\right))\mathit{E}\mathit{r}\mathit{f}(x-\frac{1}{2}+\frac{i}{2}))}{4}\}$$