\[ y''(x)-y(x) \left (a p(x)+b+\frac {p^4(x)}{30}+\frac {7 p''(x)}{3}\right )=0 \] ✗ Mathematica : cpu = 0.286493 (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
\[\left \{y \left (x \right ) = \mathit {DESol}\left (\left \{\left (-a p \left (x \right )-b -\frac {\frac {d^{4}}{d x^{4}}p \left (x \right )}{30}-\frac {7 \frac {d^{2}}{d x^{2}}p \left (x \right )}{3}\right ) \textit {\_Y} \left (x \right )+\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right \}\]