6.17   ODE No. 1550

$$\boxed{{\displaystyle x\mathit{d}\mathit{4}\mathit{y}\left(x\right)-(6x^2+1)\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+12x^3\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-(9x^2-7)x^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2(x^2-3)x^{3}y\left(x\right)=0}}$$

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

Mathematica: cpu = 7.686976 (sec), leaf count = 262 $$\left\{\{y(x)\to c_3{e}^{\frac{x^2}{2}}{\int }_1^x\frac{e^{\frac{K[1{]}^2}{2}}K[1](\int \frac{U(\frac{1}{20}(-5-9\sqrt{5}),-\frac{1}{2},\frac{1}{2}\sqrt{5}K[1{]}^2)\exp (\frac{1}{2}(-\frac{1}{2}K[1{]}^2-2\log (K[1]))-\frac{1}{4}\sqrt{5}K[1{]}^2)}{\sqrt{K[1]}\sqrt[4]{K[1{]}^2}}dK[1])}{\sqrt[4]{2}}dK[1]+c_4{e}^{\frac{x^2}{2}}{\int }_1^x\frac{e^{\frac{K[2{]}^2}{2}}K[2](\int \frac{L_{\frac{1}{20}(5+9\sqrt{5})}^{-\frac{3}{2}}(\frac{1}{2}\sqrt{5}K[2{]}^2)\exp (\frac{1}{2}(-\frac{1}{2}K[2{]}^2-2\log (K[2]))-\frac{1}{4}\sqrt{5}K[2{]}^2)}{\sqrt{K[2]}\sqrt[4]{K[2{]}^2}}dK[2])}{\sqrt[4]{2}}dK[2]+c_1{e}^{\frac{x^2}{2}}+c_2{e}^{x^2}\}\right\}$$

Maple: cpu = 0.390 (sec), leaf count = 159 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{x^2}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{x^2}{2}}+\mathit{\_}\mathit{C}\mathit{3}(-{\mathrm{e}}^{x^2}\int 1{\mathit{M}}_{\frac{9\sqrt{5}}{20},\frac{3}{4}}\left(\frac{\sqrt{5}{x}^2}{2}\right){\mathrm{e}}^{-\frac{x^2}{4}}{x}^{-\frac{3}{2}}\mathrm{d}x+\int 1{\mathit{M}}_{\frac{9\sqrt{5}}{20},\frac{3}{4}}\left(\frac{\sqrt{5}{x}^2}{2}\right){\mathrm{e}}^{\frac{x^2}{4}}{x}^{-\frac{3}{2}}\mathrm{d}x{\mathrm{e}}^{\frac{x^2}{2}})+\mathit{\_}\mathit{C}\mathit{4}(-{\mathrm{e}}^{x^2}\int 1{\mathit{W}}_{\frac{9\sqrt{5}}{20},\frac{3}{4}}\left(\frac{\sqrt{5}{x}^2}{2}\right){\mathrm{e}}^{-\frac{x^2}{4}}{x}^{-\frac{3}{2}}\mathrm{d}x+\int 1{\mathit{W}}_{\frac{9\sqrt{5}}{20},\frac{3}{4}}\left(\frac{\sqrt{5}{x}^2}{2}\right){\mathrm{e}}^{\frac{x^2}{4}}{x}^{-\frac{3}{2}}\mathrm{d}x{\mathrm{e}}^{\frac{x^2}{2}})\}$$