\[ y''(x)=\frac {\phi '(x) y'(x)}{\phi (x)-\phi (a)}-\frac {y(x) \left (\phi ''(a)-n (n+1) (\phi (x)-\phi (a))^2\right )}{\phi (x)-\phi (a)} \] ✗ Mathematica : cpu = 0.862216 (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
\[\left \{y \left (x \right ) = \mathit {DESol}\left (\left \{-\frac {\left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right ) \left (\frac {d}{d x}\phi \left (x \right )\right )}{-\phi \left (a \right )+\phi \left (x \right )}+\frac {\left (-\left (n +1\right ) \left (-\phi \left (a \right )+\phi \left (x \right )\right )^{2} n +\frac {d^{2}}{d a^{2}}\phi \left (a \right )\right ) \textit {\_Y} \left (x \right )}{-\phi \left (a \right )+\phi \left (x \right )}+\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right \}\]