2.1445   ODE No. 1445

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

$$y^{″}(x)=-\frac{y(x)((g(x{)}^2-1)(f^{\prime }(x)(2f^{\prime }(x)g^{\prime }(x)+f(x)g^{″}(x))-f(x)f^{″}(x)g^{\prime }(x))-f(x)g^{\prime }(x{)}^2(2g(x)f^{\prime }(x)+v(v+1)f(x)g^{\prime }(x)))}{f(x{)}^2(g(x{)}^2-1)g^{\prime }(x)}-\frac{y^{\prime }(x)(2f(x)g(x)g^{\prime }(x{)}^2-(g(x{)}^2-1)(2f^{\prime }(x)g^{\prime }(x)+f(x)g^{″}(x)))}{f(x)(g(x{)}^2-1)g^{\prime }(x)}$$ ✓ Mathematica : cpu = 0.143837 (sec), leaf count = 24

$$\{\{y(x)\to c_{1}f(x)P_v(g(x))+c_{2}f(x)Q_v(g(x))\}\}$$ ✓ Maple : cpu = 0.448 (sec), leaf count = 20

$$\{y\left(x\right)=f\left(x\right)(\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(v,g\left(x\right))\mathit{\_}\mathit{C}\mathit{2}+\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(v,g\left(x\right))\mathit{\_}\mathit{C}\mathit{1})\}$$