\[ 3 y^{(4)}(x) y''(x)-5 y^{(3)}(x)^2=0 \] ✓ Mathematica : cpu = 0.114694 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_2 \left (-\sqrt {2 x+3 c_1}\right )+c_4 x+c_3\right \}\right \}\] ✓ Maple : cpu = 0.341 (sec), leaf count = 28
\[y \relax (x ) = 3 \left (x +c_{2}\right ) \sqrt {6}\, c_{1} \sqrt {-\frac {c_{1}}{x +c_{2}}}+c_{3} x +c_{4}\]