\[ y''(x)=\frac {\phi '(x) y'(x)}{\phi (x)-\phi (a)}-\frac {y(x) \left (\phi ''(a)-n (n+1) (\phi (x)-\phi (a))^2\right )}{\phi (x)-\phi (a)} \] ✗ Mathematica : cpu = 0.86219 (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
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) -{\frac { \left ( {\frac {\rm d}{{\rm d}x}}\phi \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{\phi \left ( x \right ) -\phi \left ( a \right ) }}+{\frac { \left ( -n \left ( n+1 \right ) \left ( \phi \left ( x \right ) -\phi \left ( a \right ) \right ) ^{2}+{\frac {{\rm d}^{2}}{{\rm d}{a}^{2}}}\phi \left ( a \right ) \right ) {\it \_Y} \left ( x \right ) }{\phi \left ( x \right ) -\phi \left ( a \right ) }} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]