6.22   ODE No. 1555

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

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

Mathematica: cpu = 0.060008 (sec), leaf count = 156 $$\left\{\{y(x)\to c_4{G}_{0,4}^{2,0}\left(\frac{{\lambda }^2{x}^2}{16}|\begin{array}{c}-\frac{1}{2},\frac{1}{2},0,0\end{array}\right)+c_2{G}_{0,4}^{2,0}\left(\frac{{\lambda }^2{x}^2}{16}|\begin{array}{c}0,0,-\frac{1}{2},\frac{1}{2}\end{array}\right)+\frac{c_1(J_1\left(2\sqrt{\lambda }\sqrt{x}\right)+I_1\left(2\sqrt{\lambda }\sqrt{x}\right))}{2\sqrt{\lambda }\sqrt{x}}-\frac{i{c}_3(I_1\left(2\sqrt{\lambda }\sqrt{x}\right)-J_1\left(2\sqrt{\lambda }\sqrt{x}\right))}{4\sqrt{\lambda }\sqrt{x}}\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 69 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_1\left(2\sqrt{\lambda }\sqrt{x}\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_1\left(2\sqrt{\lambda }\sqrt{x}\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{3}{\mathit{J}}_1\left(2\sqrt{-\lambda }\sqrt{x}\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{4}{\mathit{Y}}_1\left(2\sqrt{-\lambda }\sqrt{x}\right)\frac{1}{\sqrt{x}}\}$$