2.1571   ODE No. 1571

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

$$-\frac{1}{16}{b}^4{x}^{2/v}y(x)+{\nu }^4{x}^4{y}^{(4)}(x)+{\nu }^3(4\nu -2)x^3{y}^{(3)}(x)+(\nu -1){\nu }^2(2\nu -1)x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0913721 (sec), leaf count = 389

$$\left\{\{y(x)\to c_1{}_0{F}_3(;1-\frac{v}{2},1-\frac{v}{2\nu },-\frac{v}{2\nu }-\frac{v}{2}+1;\frac{b^4{v}^4{x}^{2/v}}{256{\nu }^4})+c_2{\left(\frac{i}{16}\right)}^v{v}^{2v}{b}^{2v}{\nu }^{-2v}{\left(x^{2/v}\right)}^{v/2}{}_0{F}_3(;\frac{v}{2}+1,1-\frac{v}{2\nu },-\frac{v}{2\nu }+\frac{v}{2}+1;\frac{b^4{v}^4{x}^{2/v}}{256{\nu }^4})+c_3{\left(\frac{i}{16}\right)}^{\frac{v}{\nu }}{v}^{\frac{2v}{\nu }}{\nu }^{-\frac{2v}{\nu }}{b}^{\frac{2v}{\nu }}{\left(x^{2/v}\right)}^{\frac{v}{2\nu }}{}_0{F}_3(;1-\frac{v}{2},\frac{v}{2\nu }+1,\frac{v}{2\nu }-\frac{v}{2}+1;\frac{b^4{v}^4{x}^{2/v}}{256{\nu }^4})+c_4{\left(\frac{i}{16}\right)}^{(\frac{1}{\nu }+1)v}{v}^{\frac{2(\nu +1)v}{\nu }}{\nu }^{-\frac{2(\nu +1)v}{\nu }}{b}^{\frac{2(\nu +1)v}{\nu }}{\left(x^{2/v}\right)}^{\frac{(\nu +1)v}{2\nu }}{}_0{F}_3(;\frac{v}{2}+1,\frac{v}{2\nu }+1,\frac{v}{2\nu }+\frac{v}{2}+1;\frac{b^4{v}^4{x}^{2/v}}{256{\nu }^4})\}\right\}$$

✓ Maple : cpu = 0.4 (sec), leaf count = 143

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