6.24   ODE No. 1557

$$\boxed{{\displaystyle x^2\mathit{d}\mathit{4}\mathit{y}\left(x\right)+8x\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+12\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-{\lambda }^{2}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.063008 (sec), leaf count = 146 $$\left\{\{y(x)\to c_4{G}_{0,4}^{2,0}\left(\frac{{\lambda }^2{x}^2}{16}|\begin{array}{c}-1,0,-\frac{1}{2},\frac{1}{2}\end{array}\right)+c_2{G}_{0,4}^{2,0}\left(\frac{{\lambda }^2{x}^2}{16}|\begin{array}{c}-\frac{1}{2},\frac{1}{2},-1,0\end{array}\right)-\frac{3i{c}_1(I_2\left(2\sqrt{\lambda }\sqrt{x}\right)-J_2\left(2\sqrt{\lambda }\sqrt{x}\right))}{4\lambda x}-\frac{c_3(J_2\left(2\sqrt{\lambda }\sqrt{x}\right)+I_2\left(2\sqrt{\lambda }\sqrt{x}\right))}{\lambda x}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 69 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}{\mathit{J}}_2\left(2\sqrt{\lambda }\sqrt{x}\right)+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x}{\mathit{Y}}_2\left(2\sqrt{\lambda }\sqrt{x}\right)+\frac{\mathit{\_}\mathit{C}\mathit{3}}{x}{\mathit{J}}_2\left(2\sqrt{-\lambda }\sqrt{x}\right)+\frac{\mathit{\_}\mathit{C}\mathit{4}}{x}{\mathit{Y}}_2\left(2\sqrt{-\lambda }\sqrt{x}\right)\}$$