\[ y(x) \left (-4 a n p(x)^2+a+b p(x)\right )+a p''(x) y'(x)+y''(x)=0 \] ✗ Mathematica : cpu = 0.346867 (sec), leaf count = 0 , could not solve
DSolve[(a + b*p[x] - 4*a*n*p[x]^2)*y[x] + a*Derivative[1][y][x]*Derivative[2][p][x] + Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[\{y \left (x \right ) = \mathit {DESol}\left (\left \{a \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right ) \left (\frac {d^{2}}{d x^{2}}p \left (x \right )\right )+\left (-4 a n p \left (x \right )^{2}+b p \left (x \right )+a \right ) \textit {\_Y} \left (x \right )+\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\}\]