60.8.2 problem 1838

Internal problem ID [11837]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 7, non-linear third and higher order
Problem number : 1838
Date solved : Monday, January 27, 2025 at 11:43:29 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime } y-{y^{\prime }}^{2}+1&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[1 - D[y[x],x]^2 + y[x]*D[y[x],{x,2}] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved