Internal problem ID [9417]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1838.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+1=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+1=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[1 - y'[x]^2 + y[x]*y''[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved