Internal problem ID [3231]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 89.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {y-x y^{\prime }+x^{2} {y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 123
dsolve(y(x)=x*diff(y(x),x)-x^2* (diff(y(x),x))^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -x^{2} \operatorname {RootOf}\left (4 \textit {\_Z}^{4} c_{1} x^{2}+8 \textit {\_Z}^{2} c_{1} x -\textit {\_Z} +4 c_{1} \right )^{3}+x \operatorname {RootOf}\left (4 \textit {\_Z}^{4} c_{1} x^{2}+8 \textit {\_Z}^{2} c_{1} x -\textit {\_Z} +4 c_{1} \right ) \\ y \left (x \right ) &= -x^{2} \operatorname {RootOf}\left (4 \textit {\_Z}^{4} c_{1} x^{2}-16 \textit {\_Z}^{2} c_{1} x -\textit {\_Z} +16 c_{1} \right )^{3}+x \operatorname {RootOf}\left (4 \textit {\_Z}^{4} c_{1} x^{2}-16 \textit {\_Z}^{2} c_{1} x -\textit {\_Z} +16 c_{1} \right ) \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]==x*y'[x]-x^2*(y'[x])^3,y[x],x,IncludeSingularSolutions -> True]
Timed out