\[ y(x) \left (-4 a n p(x)^2+a+b p(x)\right )+a p''(x) y'(x)+y''(x)=0 \] ✗ Mathematica : cpu = 0.304841 (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
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +a \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}p \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( a+bp \left ( x \right ) -4\,na \left ( p \left ( x \right ) \right ) ^{2} \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]