5.33   ODE No. 1481

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

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

Mathematica: cpu = 0.985125 (sec), leaf count = 431 $$\left\{\{y(x)\to -\frac{1}{240}{e}^{-\frac{x^2}{2}}(-240x^5({\int }_1^x(\frac{1}{15}\sqrt{\frac{\pi }{2}}K[1]\text{erfi}\left(\frac{K[1]}{\sqrt{2}}\right)f(K[1])-\frac{1}{240}(15\text{Ei}\left(\frac{K[1{]}^2}{2}\right)+16e^{\frac{K[1{]}^2}{2}})f(K[1])+\frac{7e^{\frac{K[1{]}^2}{2}}f(K[1])}{120K[1{]}^2}+\frac{e^{\frac{K[1{]}^2}{2}}f(K[1])}{20K[1{]}^4})dK[1])-8\sqrt{2\pi }{x}^5\text{erfi}\left(\frac{x}{\sqrt{2}}\right)({\int }_1^{x}K[2](-f(K[2]))dK[2])-15x^5\text{Ei}\left(\frac{x^2}{2}\right)({\int }_1^{x}f(K[3])dK[3])+16e^{\frac{x^2}{2}}{x}^2({\int }_1^{x}K[2](-f(K[2]))dK[2])+60e^{\frac{x^2}{2}}x({\int }_1^{x}f(K[3])dK[3])+48e^{\frac{x^2}{2}}{\int }_1^{x}K[2](-f(K[2]))dK[2]+16e^{\frac{x^2}{2}}{x}^4({\int }_1^{x}K[2](-f(K[2]))dK[2])+30e^{\frac{x^2}{2}}{x}^3({\int }_1^{x}f(K[3])dK[3]))+\frac{1}{30}{c}_2{e}^{-\frac{x^2}{2}}(\sqrt{2\pi }{x}^5\text{erfi}\left(\frac{x}{\sqrt{2}}\right)-2e^{\frac{x^2}{2}}(x^4+x^2+3))+c_3{e}^{-\frac{x^2}{2}}{x}^5(\frac{\text{Ei}\left(\frac{x^2}{2}\right)}{16}+e^{\frac{x^2}{2}}(-\frac{1}{4x^4}-\frac{1}{8x^2}))+c_1{e}^{-\frac{x^2}{2}}{x}^5\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 44 $$\{y\left(x\right)=(\mathit{\_}\mathit{C}\mathit{3}+\int \frac{2x\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}-\int \int -f\left(x\right)\mathrm{d}x\mathrm{d}x}{x^6}{\mathrm{e}}^{\frac{x^2}{2}}\mathrm{d}x){\mathrm{e}}^{-\frac{x^2}{2}}{x}^5\}$$