5.62   ODE No. 1510

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

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

Mathematica: cpu = 0.052007 (sec), leaf count = 60 $$\text{DSolve}[y(x)(a(\nu -1)x^{2\nu }+b{x}^{3\nu }+{\nu }^2-1)+x(a{x}^{2\nu }-{\nu }^2+1)y^{\prime }(x)+x^3{y}^{(3)}(x)=0,y(x),x]$$

Maple: cpu = 0.078 (sec), leaf count = 74 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{x^3\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}\mathit{\_}\mathit{Y}\left(x\right)+(x^{2\nu }ax-{\nu }^{2}x+x)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+(x^{2\nu }a\nu -a{x}^{2\nu }+b{x}^{3\nu }+{\nu }^2-1)\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$