ODE
\[ 3 y''(x) y''''(x)=5 \left (y'''(x)\right )^2 \] ODE Classification
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.28994 (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 = 2.696 (sec), leaf count = 28
\[\left [y \left (x \right ) = 3 \left (x +\textit {\_C2} \right ) \sqrt {6}\, \textit {\_C1} \sqrt {-\frac {\textit {\_C1}}{x +\textit {\_C2}}}+\textit {\_C3} x +\textit {\_C4}\right ]\] Mathematica raw input
DSolve[3*y''[x]*y''''[x] == 5*y'''[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[2*x + 3*C[1]]*C[2]) + C[3] + x*C[4]}}
Maple raw input
dsolve(3*diff(diff(y(x),x),x)*diff(diff(diff(diff(y(x),x),x),x),x) = 5*diff(diff(diff(y(x),x),x),x)^2, y(x))
Maple raw output
[y(x) = 3*(x+_C2)*6^(1/2)*_C1*(-_C1/(x+_C2))^(1/2)+_C3*x+_C4]