\[ y''(x)=\frac {\phi '(x) y'(x)}{\phi (x)-\phi (a)}-\frac {y(x) \left (\phi ''(a)-n (n+1) (\phi (x)-\phi (a))^2\right )}{\phi (x)-\phi (a)} \] ✗ Mathematica : cpu = 0.648182 (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 or ODESolStruc
\[y \relax (x ) = \mathit {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \relax (x )-\frac {\left (\frac {d}{d x}\phi \relax (x )\right ) \left (\frac {d}{d x}\textit {\_Y} \relax (x )\right )}{\phi \relax (x )-\phi \relax (a )}+\frac {\left (-n \left (n +1\right ) \left (\phi \relax (x )-\phi \relax (a )\right )^{2}+\frac {d^{2}}{d a^{2}}\phi \relax (a )\right ) \textit {\_Y} \relax (x )}{\phi \relax (x )-\phi \relax (a )}\right \}, \left \{\textit {\_Y} \relax (x )\right \}\right )\]