Internal problem ID [9429]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1850.
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]]
Solve \begin {gather*} \boxed {y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+\left (y^{\prime }\right )^{3} y^{\prime \prime \prime }=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)*diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(y(x),x),x)*diff(diff(diff(y(x),x),x),x)+diff(y(x),x)^3*diff(diff(diff(y(x),x),x),x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]^3*Derivative[3][y][x] - y''[x]*Derivative[3][y][x] + y'[x]*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved