2.1558   ODE No. 1558

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

$$-\frac{1}{16}{b}^{4}y(x)+(n-\nu +1)(n-\nu +2)y^{″}(x)+x(2n-2\nu +4)y^{(3)}(x)+x^2{y}^{(4)}(x)=0$$ ✓ Mathematica : cpu = 0.116547 (sec), leaf count = 319

$$\left\{\{y(x)\to c_1{2}^{n-\nu -1}{b}^{\nu -n}{x}^{\frac{\nu -n}{2}}\mathrm{\Gamma }(n-\nu +1)(J_{n-\nu }\left(b\sqrt{x}\right)+I_{n-\nu }\left(b\sqrt{x}\right))+c_4{i}^{-n+\nu +1}{2}^{3n-3\nu -3}{b}^{2(-n+\nu +1)+n-\nu -2}{x}^{\frac{1}{2}(n-\nu -2)-n+\nu +1}\mathrm{\Gamma }(-n+\nu +2)(I_{\nu -n}\left(b\sqrt{x}\right)-J_{\nu -n}\left(b\sqrt{x}\right))+c_3{i}^{\nu -n}{2}^{3n-3\nu -1}{b}^{2(\nu -n)+n-\nu }{x}^{\frac{n-\nu }{2}-n+\nu }\mathrm{\Gamma }(-n+\nu +1)(J_{\nu -n}\left(b\sqrt{x}\right)+I_{\nu -n}\left(b\sqrt{x}\right))+i{c}_2{2}^{n-\nu -3}{b}^{\nu -n}{x}^{\frac{1}{2}(-n+\nu -2)+1}\mathrm{\Gamma }(n-\nu +2)(I_{n-\nu }\left(b\sqrt{x}\right)-J_{n-\nu }\left(b\sqrt{x}\right))\}\right\}$$ ✓ Maple : cpu = 0.19 (sec), leaf count = 67

$$\{y\left(x\right)=x^{-\frac{n}{2}+\frac{\nu }{2}}({\mathit{K}}_{n-\nu }\left(b\sqrt{x}\right)\mathit{\_}\mathit{C}\mathit{3}+{\mathit{I}}_{n-\nu }\left(b\sqrt{x}\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{J}}_{n-\nu }\left(b\sqrt{x}\right)\mathit{\_}\mathit{C}\mathit{2}+{\mathit{Y}}_{n-\nu }\left(b\sqrt{x}\right)\mathit{\_}\mathit{C}\mathit{4})\}$$