Internal problem ID [6501]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 29.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {\left (y-2 y^{\prime } x \right )^{2}-\left (y^{\prime }\right )^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.438 (sec). Leaf size: 75
dsolve((y(x)-2*x*diff(y(x),x))^2= diff(y(x),x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ \left [x \left (\textit {\_T} \right ) = \frac {\frac {3 \textit {\_T}^{\frac {5}{2}}}{5}+c_{1}}{\textit {\_T}^{2}}, y \left (\textit {\_T} \right ) = \frac {\frac {6 \textit {\_T}^{\frac {5}{2}}}{5}+2 c_{1}}{\textit {\_T}}-\textit {\_T}^{\frac {3}{2}}\right ] \\ \left [x \left (\textit {\_T} \right ) = \frac {-\frac {3 \textit {\_T}^{\frac {5}{2}}}{5}+c_{1}}{\textit {\_T}^{2}}, y \left (\textit {\_T} \right ) = \frac {-\frac {6 \textit {\_T}^{\frac {5}{2}}}{5}+2 c_{1}}{\textit {\_T}}+\textit {\_T}^{\frac {3}{2}}\right ] \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y[x]-2*x*y'[x])^2== y'[x]^3,y[x],x,IncludeSingularSolutions -> True]
Timed out