6.35   ODE No. 1568

$$\boxed{{\displaystyle x^4\mathit{d}\mathit{4}\mathit{y}\left(x\right)+8x^3\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+12x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+ay\left(x\right)=0}}$$

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

Mathematica: cpu = 0.157020 (sec), leaf count = 378 $$\left\{\{y(x)\to c_1{b}^{\frac{a-c\mu -c\nu }{c}}{\left(x^{2c}\right)}^{\frac{a-c\mu -c\nu }{2c}}{}_2{F}_3(-\frac{\mu }{2}-\frac{\nu }{2}+\frac{1}{2},-\frac{\mu }{2}-\frac{\nu }{2}+1;1-\mu ,1-\nu ,-\mu -\nu +1;-b^2{x}^{2c})+c_2{b}^{\frac{a+c\mu -c\nu }{c}}{\left(x^{2c}\right)}^{\frac{a+c\mu -c\nu }{2c}}{}_2{F}_3(\frac{\mu }{2}-\frac{\nu }{2}+\frac{1}{2},\frac{\mu }{2}-\frac{\nu }{2}+1;\mu +1,1-\nu ,\mu -\nu +1;-b^2{x}^{2c})+c_3{b}^{\frac{a-c\mu +c\nu }{c}}{\left(x^{2c}\right)}^{\frac{a-c\mu +c\nu }{2c}}{}_2{F}_3(-\frac{\mu }{2}+\frac{\nu }{2}+\frac{1}{2},-\frac{\mu }{2}+\frac{\nu }{2}+1;1-\mu ,\nu +1,-\mu +\nu +1;-b^2{x}^{2c})+c_4{b}^{\frac{a+c\mu +c\nu }{c}}{\left(x^{2c}\right)}^{\frac{a+c\mu +c\nu }{2c}}{}_2{F}_3(\frac{\mu }{2}+\frac{\nu }{2}+\frac{1}{2},\frac{\mu }{2}+\frac{\nu }{2}+1;\mu +1,\nu +1,\mu +\nu +1;-b^2{x}^{2c})\}\right\}$$

Maple: cpu = 0.015 (sec), leaf count = 89 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{1}{2}-\frac{1}{2}\sqrt{5-4\sqrt{1-a}}}+\mathit{\_}\mathit{C}\mathit{2}{x}^{-\frac{1}{2}+\frac{1}{2}\sqrt{5-4\sqrt{1-a}}}+\mathit{\_}\mathit{C}\mathit{3}{x}^{-\frac{1}{2}-\frac{1}{2}\sqrt{5+4\sqrt{1-a}}}+\mathit{\_}\mathit{C}\mathit{4}{x}^{-\frac{1}{2}+\frac{1}{2}\sqrt{5+4\sqrt{1-a}}}\}$$