2.1037   ODE No. 1037

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

$$a{y}^{\prime }(x)+y(x)(-(b^2{x}^2+c))+y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0295953 (sec), leaf count = 101

$$\left\{\{y(x)\to c_1{e}^{-\frac{ax}{2}-\frac{b{x}^2}{2}}{H}_{\frac{-a^2-4b-4c}{8b}}\left(\sqrt{b}x\right)+c_2{e}^{-\frac{ax}{2}-\frac{b{x}^2}{2}}{}_1{F}_1(-\frac{-a^2-4b-4c}{16b};\frac{1}{2};b{x}^2)\}\right\}$$

✓ Maple : cpu = 0.099 (sec), leaf count = 73

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{M}(\frac{a^2+12b+4c}{16b},\frac{3}{2},b{x}^2)x{\mathrm{e}}^{-\frac{x(bx+a)}{2}}+\mathit{\_}\mathit{C}\mathit{2}\mathit{U}(\frac{a^2+12b+4c}{16b},\frac{3}{2},b{x}^2)x{\mathrm{e}}^{-\frac{x(bx+a)}{2}}\}$$