\[ 3 y^{(4)}(x) y''(x)-5 y^{(3)}(x)^2=0 \] ✓ Mathematica : cpu = 0.130194 (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 = 0.416 (sec), leaf count = 28
\[\left \{y \left (x \right ) = c_{3} x +3 c_{1} \left (c_{2}+x \right ) \sqrt {6}\, \sqrt {-\frac {c_{1}}{c_{2}+x}}+c_{4}\right \}\]