5.30   ODE No. 1478

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

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

Mathematica: cpu = 0.032004 (sec), leaf count = 104 $$\left\{\{y(x)\to -\frac{2(-1{)}^{3/4}\sqrt{2}{c}_1{}_0{F}_2(;\frac{1}{2},\frac{3}{4};\frac{a{x}^4}{64})}{\sqrt[4]{a}x}+c_2{}_0{F}_2(;\frac{3}{4},\frac{5}{4};\frac{a{x}^4}{64})+\frac{\sqrt[4]{-1}\sqrt[4]{a}{c}_{3}x{}_0{F}_2(;\frac{5}{4},\frac{3}{2};\frac{a{x}^4}{64})}{2\sqrt{2}}\}\right\}$$

Maple: cpu = 0.094 (sec), leaf count = 48 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_0\text{F}{}_2(;\frac{3}{4},\frac{5}{4};\frac{a{x}^4}{64})+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x}{}_0\text{F}{}_2(;\frac{1}{2},\frac{3}{4};\frac{a{x}^4}{64})+\mathit{\_}\mathit{C}\mathit{3}x{}_0\text{F}{}_2(;\frac{5}{4},\frac{3}{2};\frac{a{x}^4}{64})\}$$