6.33   ODE No. 1566

$$\boxed{{\displaystyle x^4\mathit{d}\mathit{4}\mathit{y}\left(x\right)+6x^3\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+(4x^4+(-2{\mu }^2-2{\nu }^2+7)x^2)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(16x^3+(-2{\mu }^2-2{\nu }^2+1)x)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(8x^2+{({\mu }^2-{\nu }^2)}^2)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.620079 (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 = 0.156 (sec), leaf count = 37 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{\nu }\left(x\right){\mathit{J}}_{\mu }\left(x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathit{J}}_{\nu }\left(x\right){\mathit{Y}}_{\mu }\left(x\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathit{Y}}_{\nu }\left(x\right){\mathit{J}}_{\mu }\left(x\right)+\mathit{\_}\mathit{C}\mathit{4}{\mathit{Y}}_{\nu }\left(x\right){\mathit{Y}}_{\mu }\left(x\right)\}$$