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 = 0.0315989 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_2 \left (-\sqrt {3 c_1+2 x}\right )+c_4 x+c_3\right \}\right \}\]
Maple ✓
cpu = 0.291 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) =3\, \left ( x+{\it \_C2} \right ) \sqrt {6}{{\it \_C1}}^{2}\sqrt {-{\frac {{\it \_C1}}{x+{\it \_C2}}}}+{\it \_C3}\,x+{\it \_C4} \right \} \] 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),'implicit')
Maple raw output
y(x) = 3*(x+_C2)*6^(1/2)*_C1^2*(-_C1/(x+_C2))^(1/2)+_C3*x+_C4