4.306   ODE No. 1306

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

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

Mathematica: cpu = 1.002127 (sec), leaf count = 56 $$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {unicode {f818}''(unicode {f817}) unicode {f817}^3+unicode {f818}'(unicode {f817}) unicode {f817}^2+left (a unicode {f817}^2+b unicode {f817}+aright ) unicode {f818}(unicode {f817})=0,unicode {f818}(1)=c\_1,unicode {f818}'(1)=c\_2right }right )(x)right }right }}$$

Maple: cpu = 0.109 (sec), leaf count = 95 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{D}(0,8a+4b,0,8a-4b,\frac{1+x}{x-1})+\mathit{\_}\mathit{C}\mathit{2}\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{D}(0,8a+4b,0,8a-4b,\frac{1+x}{x-1})\int \frac{1}{x}{\left(\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{D}(0,8a+4b,0,8a-4b,\frac{1+x}{x-1})\right)}^{-2}\mathrm{d}x\}$$