2.1439   ODE No. 1439

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

$$y^{″}(x)=\frac{{\varphi }^{\prime }(x)y^{\prime }(x)}{\varphi (x)-\varphi (a)}-\frac{y(x)({\varphi }^{″}(a)-n(n+1)(\varphi (x)-\varphi (a){)}^2)}{\varphi (x)-\varphi (a)}$$ ✗ Mathematica : cpu = 0.819674 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == (Derivative[1][phi][x]*Derivative[1][y][x])/(-phi[a] + phi[x]) - (y[x]*(-(n*(1 + n)*(-phi[a] + phi[x])^2) + Derivative[2][phi][a]))/(-phi[a] + phi[x]), y[x], x]

✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol

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