2.1572   ODE No. 1572

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

$$(-2(x^2-1)(\mu (\mu +1)+\nu (\nu +1))+24x^3-8)y^{″}(x)-6x(\mu (\mu +1)+\nu (\nu +1)-2)y^{\prime }(x)+((\mu (\mu +1)-\nu (\nu +1){)}^2-2\mu (\mu +1)-2\nu (\nu +1))y(x)+{(x^2-1)}^2{y}^{(4)}(x)+10x(x^2-1)y^{(3)}(x)=0$$ ✗ Mathematica : cpu = 87.5806 (sec), leaf count = 0 , DifferentialRoot result

$$\left\{\{y(x)\to (x)\}\right\}$$

✓ Maple : cpu = 0.396 (sec), leaf count = 35

$$\{y\left(x\right)=(c_1\mathrm{LegendreP}(\mu ,x)+c_2\mathrm{LegendreQ}(\mu ,x))\mathrm{LegendreP}(\nu ,x)+(c_3\mathrm{LegendreP}(\mu ,x)+c_4\mathrm{LegendreQ}(\mu ,x))\mathrm{LegendreQ}(\nu ,x)\}$$