5.3   ODE No. 1451

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)-a{x}^{b}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.019502 (sec), leaf count = 168 $$\left\{\{y(x)\to (-1{)}^{\frac{1}{b+3}}(b+3{)}^{-\frac{3}{b+3}}{c}_{2}x{a}^{\frac{1}{b+3}}{}_0{F}_2(;1-\frac{1}{b+3},1+\frac{1}{b+3};\frac{a{x}^{b+3}}{(b+3{)}^3})+(-1{)}^{\frac{2}{b+3}}(b+3{)}^{-\frac{6}{b+3}}{c}_3{x}^2{a}^{\frac{2}{b+3}}{}_0{F}_2(;1+\frac{1}{b+3},1+\frac{2}{b+3};\frac{a{x}^{b+3}}{(b+3{)}^3})+c_1{}_0{F}_2(;1-\frac{2}{b+3},1-\frac{1}{b+3};\frac{a{x}^{b+3}}{(b+3{)}^3})\}\right\}$$

Maple: cpu = 0.093 (sec), leaf count = 114 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_0\text{F}{}_2(;\frac{b+2}{b+3},\frac{b+1}{b+3};\frac{x^{b+3}a}{{(b+3)}^3})+\mathit{\_}\mathit{C}\mathit{2}x{}_0\text{F}{}_2(;\frac{b+4}{b+3},\frac{b+2}{b+3};\frac{x^{b+3}a}{{(b+3)}^3})+\mathit{\_}\mathit{C}\mathit{3}{x}^2{}_0\text{F}{}_2(;\frac{b+5}{b+3},\frac{b+4}{b+3};\frac{x^{b+3}a}{{(b+3)}^3})\}$$