2.1555   ODE No. 1555

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

$${\lambda }^2(-y(x))+x^2{y}^{(4)}(x)+6y^{″}(x)+6x{y}^{(3)}(x)=0$$ ✓ Mathematica : cpu = 0.0451337 (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 = 0.448 (sec), leaf count = 61

$$\{y\left(x\right)=(\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_1\left(2\sqrt{\lambda }\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_1\left(2\sqrt{\lambda }\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathit{J}}_1\left(2\sqrt{-\lambda }\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{4}{\mathit{Y}}_1\left(2\sqrt{-\lambda }\sqrt{x}\right))\frac{1}{\sqrt{x}}\}$$