\[ y''(x)=\frac {\phi '(x) y'(x)}{\phi (x)-\phi (a)}-\frac {y(x) \left (\phi ''(a)-n (n+1) (\phi (x)-\phi (a))^2\right )}{\phi (x)-\phi (a)} \] ✗ Mathematica : cpu = 0.648182 (sec), leaf count = 0
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]
, 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
dsolve(diff(diff(y(x),x),x) = diff(phi(x),x)/(phi(x)-phi(a))*diff(y(x),x)-(-n*(n+1)*(phi(x)-phi(a))^2+(D@@2)(phi)(a))/(phi(x)-phi(a))*y(x),y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )-\frac {\left (\frac {d}{d x}\phi \left (x \right )\right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )}{\phi \left (x \right )-\phi \left (a \right )}+\frac {\left (-n \left (n +1\right ) \left (\phi \left (x \right )-\phi \left (a \right )\right )^{2}+\frac {d^{2}}{d a^{2}}\phi \left (a \right )\right ) \textit {\_Y} \left (x \right )}{\phi \left (x \right )-\phi \left (a \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]