2.1510   ODE No. 1510

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

$$y(x)(a(\nu -1)x^{2\nu }+b{x}^{3\nu }+{\nu }^2-1)+x(a{x}^{2\nu }-{\nu }^2+1)y^{\prime }(x)+x^3{y}^{(3)}(x)=0$$ ✓ Mathematica : cpu = 0.0353295 (sec), leaf count = 102

$$\left\{\{y(x)\to c_1{x}^{1-\nu }{e}^{\frac{x^{\nu }\text{Root}[{\mathrm{\#}\text{1}}^3+\mathrm{\#}\text{1}a+b\mathrm{\&},1]}{\nu }}+c_2{x}^{1-\nu }{e}^{\frac{x^{\nu }\text{Root}[{\mathrm{\#}\text{1}}^3+\mathrm{\#}\text{1}a+b\mathrm{\&},2]}{\nu }}+c_3{x}^{1-\nu }{e}^{\frac{x^{\nu }\text{Root}[{\mathrm{\#}\text{1}}^3+\mathrm{\#}\text{1}a+b\mathrm{\&},3]}{\nu }}\}\right\}$$ ✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol

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