5.52   ODE No. 1500

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

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

Mathematica: cpu = 47.362014 (sec), leaf count = 71 $$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {unicode {f818}^{(3)}(unicode {f817}) unicode {f817}^2-(unicode {f817}+v) unicode {f818}''(unicode {f817}) unicode {f817}-(unicode {f817}+1) nu unicode {f818}(unicode {f817})+(2 unicode {f817} nu +nu ) unicode {f818}'(unicode {f817})=0,unicode {f818}(1)=c\_1,unicode {f818}'(1)=c\_2,unicode {f818}''(1)=c\_3right }right )(x)right }right }}$$

Maple: cpu = 0.172 (sec), leaf count = 55 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{2}{x}^{\frac{\nu }{2}+\frac{1}{2}}{\mathit{J}}_{-\nu -1}\left(2\sqrt{\nu }\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{3}{x}^{\frac{\nu }{2}+\frac{1}{2}}{\mathit{Y}}_{-\nu -1}\left(2\sqrt{\nu }\sqrt{x}\right)\}$$