28.1.86 problem 89

Internal problem ID [4392]
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
Date solved : Monday, January 27, 2025 at 09:11:54 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y&=x y^{\prime }-x^{2} {y^{\prime }}^{3} \end{align*}

✓ Solution by Maple

Time used: 0.096 (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: 0.000 (sec). Leaf size: 0

DSolve[y[x]==x*D[y[x],x]-x^2*(D[y[x],x])^3,y[x],x,IncludeSingularSolutions -> True]
 

Timed out