Internal problem ID [7254]
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]
\[ \boxed {\left (y-2 x y^{\prime }\right )^{2}-{y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 73
dsolve((y(x)-2*x*diff(y(x),x))^2= diff(y(x),x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ \left [x \left (\textit {\_T} \right ) &= \frac {3 \textit {\_T}^{\frac {5}{2}}+5 c_{1}}{5 \textit {\_T}^{2}}, y \left (\textit {\_T} \right ) &= \frac {\textit {\_T}^{\frac {5}{2}}+10 c_{1}}{5 \textit {\_T}}\right ] \\ \left [x \left (\textit {\_T} \right ) &= \frac {-3 \textit {\_T}^{\frac {5}{2}}+5 c_{1}}{5 \textit {\_T}^{2}}, y \left (\textit {\_T} \right ) &= \frac {-\textit {\_T}^{\frac {5}{2}}+10 c_{1}}{5 \textit {\_T}}\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