5.57   ODE No. 1505

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

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

Mathematica: cpu = 62.084884 (sec), leaf count = 69 $$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {a unicode {f818}(unicode {f817})+(2 unicode {f817} a+b) unicode {f818}'(unicode {f817})+(6 unicode {f817}-3) unicode {f818}''(unicode {f817})+2 (unicode {f817}-1) unicode {f817} unicode {f818}^{(3)}(unicode {f817})=0,unicode {f818}(2)=c\_1,unicode {f818}'(2)=c\_2,unicode {f818}''(2)=c\_3right }right )(x)right }right }}$$

Maple: cpu = 0.125 (sec), leaf count = 79 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\left(\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{i}\mathit{e}\mathit{u}\mathit{C}(-\frac{a}{2}-\frac{b}{2}+1,\frac{a}{4},\arccos \left(\sqrt{x}\right))\right)}^2+\mathit{\_}\mathit{C}\mathit{2}{\left(\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{i}\mathit{e}\mathit{u}\mathit{S}(-\frac{a}{2}-\frac{b}{2}+1,\frac{a}{4},\arccos \left(\sqrt{x}\right))\right)}^2+\mathit{\_}\mathit{C}\mathit{3}\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{i}\mathit{e}\mathit{u}\mathit{C}(-\frac{a}{2}-\frac{b}{2}+1,\frac{a}{4},\arccos \left(\sqrt{x}\right))\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{i}\mathit{e}\mathit{u}\mathit{S}(-\frac{a}{2}-\frac{b}{2}+1,\frac{a}{4},\arccos \left(\sqrt{x}\right))\}$$