6.25   ODE No. 1558

$$\boxed{{\displaystyle x^2\mathit{d}\mathit{4}\mathit{y}\left(x\right)+(2n-2\nu +4)x\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+(n-\nu +1)(n-\nu +2)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-1/16b^{4}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.160520 (sec), leaf count = 319 $$\left\{\{y(x)\to c_4{i}^{-n+\nu +1}{2}^{3n-3\nu -3}{b}^{2(-n+\nu +1)+n-\nu -2}{x}^{\frac{1}{2}(n-\nu -2)-n+\nu +1}\mathrm{\Gamma }(-n+\nu +2)(I_{\nu -n}\left(b\sqrt{x}\right)-J_{\nu -n}\left(b\sqrt{x}\right))+c_3{i}^{\nu -n}{2}^{3n-3\nu -1}{b}^{2(\nu -n)+n-\nu }{x}^{\frac{n-\nu }{2}-n+\nu }\mathrm{\Gamma }(-n+\nu +1)(J_{\nu -n}\left(b\sqrt{x}\right)+I_{\nu -n}\left(b\sqrt{x}\right))+i{c}_2{2}^{n-\nu -3}{b}^{\nu -n}{x}^{\frac{1}{2}(-n+\nu -2)+1}\mathrm{\Gamma }(n-\nu +2)(I_{n-\nu }\left(b\sqrt{x}\right)-J_{n-\nu }\left(b\sqrt{x}\right))+c_1{2}^{n-\nu -1}{b}^{\nu -n}{x}^{\frac{\nu -n}{2}}\mathrm{\Gamma }(n-\nu +1)(J_{n-\nu }\left(b\sqrt{x}\right)+I_{n-\nu }\left(b\sqrt{x}\right))\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 93 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{n}{2}+\frac{\nu }{2}}{\mathit{I}}_{n-\nu }\left(b\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{2}{x}^{-\frac{n}{2}+\frac{\nu }{2}}{\mathit{J}}_{n-\nu }\left(b\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{3}{x}^{-\frac{n}{2}+\frac{\nu }{2}}{\mathit{K}}_{n-\nu }\left(b\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{4}{x}^{-\frac{n}{2}+\frac{\nu }{2}}{\mathit{Y}}_{n-\nu }\left(b\sqrt{x}\right)\}$$