\[ f''(x) y''(x)+2 y^{(3)}(x) f'(x)+f(x) y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.0605761 (sec), leaf count = 46
DSolve[Derivative[2][f][x]*Derivative[2][y][x] + 2*Derivative[1][f][x]*Derivative[3][y][x] + f[x]*Derivative[4][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \int _1^x\int _1^{K[2]}\left (\frac {c_1}{f(K[1])}+\frac {c_2 K[1]}{f(K[1])}\right )dK[1]dK[2]+c_4 x+c_3\right \}\right \}\] ✓ Maple : cpu = 0.014 (sec), leaf count = 21
dsolve(f*diff(diff(diff(diff(y(x),x),x),x),x)=0,y(x))
\[y \left (x \right ) = \frac {1}{6} x^{3} c_{1}+\frac {1}{2} x^{2} c_{2}+x c_{3}+c_{4}\]