Internal problem ID [2491]
Book: Applied Differential equations, N Curle, 1971
Section: Examples, page 35
Problem number: 3.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y-x -\left (y^{\prime }\right )^{2} \left (1-\frac {2 y^{\prime }}{3}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 35
dsolve(y(x)-x=(diff(y(x),x))^2*(1-2/3* diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = x +\frac {1}{3} \\ y \relax (x ) = c_{1}-\frac {2 \left (c_{1}-x \right )^{\frac {3}{2}}}{3} \\ y \relax (x ) = c_{1}+\frac {2 \left (c_{1}-x \right )^{\frac {3}{2}}}{3} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]-x==(y'[x])^2*(1-2/3* y'[x]),y[x],x,IncludeSingularSolutions -> True]
Timed out