2.1566   ODE No. 1566

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

$$(x(-2{\mu }^2-2{\nu }^2+1)+16x^3)y^{\prime }(x)+y(x)({({\mu }^2-{\nu }^2)}^2+8x^2)+(x^2(-2{\mu }^2-2{\nu }^2+7)+4x^4)y^{″}(x)+x^4{y}^{(4)}(x)+6x^3{y}^{(3)}(x)=0$$ ✓ Mathematica : cpu = 0.626415 (sec), leaf count = 238

$$\left\{\{y(x)\to c_1{x}^{-\mu -\nu }{}_2{F}_3(-\frac{\mu }{2}-\frac{\nu }{2}+\frac{1}{2},-\frac{\mu }{2}-\frac{\nu }{2}+1;1-\mu ,1-\nu ,-\mu -\nu +1;-x^2)+c_2{x}^{\mu -\nu }{}_2{F}_3(\frac{\mu }{2}-\frac{\nu }{2}+\frac{1}{2},\frac{\mu }{2}-\frac{\nu }{2}+1;\mu +1,1-\nu ,\mu -\nu +1;-x^2)+c_3{x}^{\nu -\mu }{}_2{F}_3(-\frac{\mu }{2}+\frac{\nu }{2}+\frac{1}{2},-\frac{\mu }{2}+\frac{\nu }{2}+1;1-\mu ,\nu +1,-\mu +\nu +1;-x^2)+c_4{x}^{\mu +\nu }{}_2{F}_3(\frac{\mu }{2}+\frac{\nu }{2}+\frac{1}{2},\frac{\mu }{2}+\frac{\nu }{2}+1;\mu +1,\nu +1,\mu +\nu +1;-x^2)\}\right\}$$

✓ Maple : cpu = 0.346 (sec), leaf count = 37

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{\nu }\left(x\right){\mathit{J}}_{\mu }\left(x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathit{J}}_{\nu }\left(x\right){\mathit{Y}}_{\mu }\left(x\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathit{Y}}_{\nu }\left(x\right){\mathit{J}}_{\mu }\left(x\right)+\mathit{\_}\mathit{C}\mathit{4}{\mathit{Y}}_{\nu }\left(x\right){\mathit{Y}}_{\mu }\left(x\right)\}$$