5.31   ODE No. 1479

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

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

Mathematica: cpu = 0.142518 (sec), leaf count = 153 $$\left\{\{y(x)\to \frac{1}{2}i{c}_{2}x{}_1{F}_2(\frac{a}{2}+\frac{1}{2};\frac{3}{2},\frac{a}{2}+\frac{b}{2}+\frac{1}{2};\frac{x^2}{4})+c_1{}_1{F}_2(\frac{a}{2};\frac{1}{2},\frac{a}{2}+\frac{b}{2};\frac{x^2}{4})+c_3{\left(\frac{i}{2}\right)}^{-a-b+2}{x}^{-a-b+2}{}_1{F}_2(1-\frac{b}{2};-\frac{a}{2}-\frac{b}{2}+\frac{3}{2},-\frac{a}{2}-\frac{b}{2}+2;\frac{x^2}{4})\}\right\}$$

Maple: cpu = 0.187 (sec), leaf count = 92 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_1\text{F}{}_2(\frac{a}{2};\frac{1}{2},\frac{a}{2}+\frac{b}{2};\frac{x^2}{4})+\mathit{\_}\mathit{C}\mathit{2}x{}_1\text{F}{}_2(\frac{1}{2}+\frac{a}{2};\frac{3}{2},\frac{a}{2}+\frac{b}{2}+\frac{1}{2};\frac{x^2}{4})+\mathit{\_}\mathit{C}\mathit{3}{x}^{-a-b+2}{}_1\text{F}{}_2(1-\frac{b}{2};2-\frac{b}{2}-\frac{a}{2},-\frac{a}{2}-\frac{b}{2}+\frac{3}{2};\frac{x^2}{4})\}$$