2.1478   ODE No. 1478

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

$$-a{x}^{2}y(x)+3y^{″}(x)+x{y}^{(3)}(x)=0$$ ✓ Mathematica : cpu = 0.0238575 (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 = 0.11 (sec), leaf count = 48

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_0\text{F}{}_2(;\frac{3}{4},\frac{5}{4};\frac{a{x}^4}{64})+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x}{}_0\text{F}{}_2(;\frac{1}{2},\frac{3}{4};\frac{a{x}^4}{64})+\mathit{\_}\mathit{C}\mathit{3}x{}_0\text{F}{}_2(;\frac{5}{4},\frac{3}{2};\frac{a{x}^4}{64})\}$$