5.7   ODE No. 1455

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)-x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(a+b-1)x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-by\left(x\right)a=0}}$$

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

Mathematica: cpu = 0.028004 (sec), leaf count = 127 $$\left\{\{y(x)\to \sqrt[3]{-\frac{1}{3}}{c}_{2}x{}_2{F}_2(\frac{1}{3}-\frac{a}{3},\frac{1}{3}-\frac{b}{3};\frac{2}{3},\frac{4}{3};\frac{x^3}{3})+c_1{}_2{F}_2(-\frac{a}{3},-\frac{b}{3};\frac{1}{3},\frac{2}{3};\frac{x^3}{3})+{(-\frac{1}{3})}^{2/3}{c}_3{x}^2{}_2{F}_2(\frac{2}{3}-\frac{a}{3},\frac{2}{3}-\frac{b}{3};\frac{4}{3},\frac{5}{3};\frac{x^3}{3})\}\right\}$$

Maple: cpu = 0.110 (sec), leaf count = 71 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_2(-\frac{a}{3},-\frac{b}{3};\frac{1}{3},\frac{2}{3};\frac{x^3}{3})+\mathit{\_}\mathit{C}\mathit{2}x{}_2\text{F}{}_2(\frac{1}{3}-\frac{a}{3},\frac{1}{3}-\frac{b}{3};\frac{2}{3},\frac{4}{3};\frac{x^3}{3})+\mathit{\_}\mathit{C}\mathit{3}{x}^2{}_2\text{F}{}_2(-\frac{a}{3}+\frac{2}{3},-\frac{b}{3}+\frac{2}{3};\frac{4}{3},\frac{5}{3};\frac{x^3}{3})\}$$