\[ y''(x)-y(x) \left (a p(x)+b+\frac {7 p''(x)}{3}+\frac {p^4(x)}{30}\right )=0 \] ✗ Mathematica : cpu = 0.214658 (sec), leaf count = 0 , could not solve
DSolve[-(y[x]*(b + a*p[x] + (p^4)[x]/30 + (7*Derivative[2][p][x])/3)) + Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) + \left ( -{\frac {{\frac {{\rm d}^{4}}{{\rm d}{x}^{4}}}p \left ( x \right ) }{30}}-{\frac {7\,{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}p \left ( x \right ) }{3}}-ap \left ( x \right ) -b \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]