Internal problem ID [9431]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1852.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]
Solve \begin {gather*} \boxed {3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 \left (y^{\prime \prime \prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 36
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=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = x c_{1}+c_{2} \\ y \relax (x ) = 3 \left (c_{2}+x \right ) \sqrt {6}\, c_{1} \sqrt {-\frac {c_{1}}{c_{2}+x}}+x c_{3}+c_{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 28
DSolve[-5*Derivative[3][y][x]^2 + 3*y''[x]*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \left (-\sqrt {2 x+3 c_1}\right )+c_4 x+c_3 \\ \end{align*}