5.49   ODE No. 1497

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

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

Mathematica: cpu = 0.499063 (sec), leaf count = 135 $$\left\{\{y(x)\to c_1{}_0{F}_2(;\frac{2}{3}-p,\frac{1}{3}-q;\frac{x^3}{27})+c_2(-1{)}^{\frac{1}{3}(3p+1)}{3}^{-3p-1}{x}^{3p+1}{}_0{F}_2(;p+\frac{4}{3},p-q+\frac{2}{3};\frac{x^3}{27})+c_3(-1{)}^{\frac{1}{3}(3q+2)}{3}^{-3q-2}{x}^{3q+2}{}_0{F}_2(;q+\frac{5}{3},-p+q+\frac{4}{3};\frac{x^3}{27})\}\right\}$$

Maple: cpu = 0.203 (sec), leaf count = 77 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_0\text{F}{}_2(;-q+\frac{1}{3},-p+\frac{2}{3};\frac{x^3}{27})+\mathit{\_}\mathit{C}\mathit{2}{x}^{1+3p}{}_0\text{F}{}_2(;p+\frac{4}{3},-q+\frac{2}{3}+p;\frac{x^3}{27})+\mathit{\_}\mathit{C}\mathit{3}{x}^{3q+2}{}_0\text{F}{}_2(;q+\frac{5}{3},q+\frac{4}{3}-p;\frac{x^3}{27})\}$$