28.1.60 problem 61

Internal problem ID [4366]
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 : 61
Date solved : Monday, January 27, 2025 at 09:09:19 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y&=\left ({\mathrm e}^{y}+2 y x -2 x \right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 62

dsolve(y(x)=(exp(y(x))+2*x*y(x)-2*x)*diff(y(x),x),y(x), singsol=all)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left (x \,\textit {\_Z}^{2}-c_{1} +\textit {\_Z} +{\mathrm e}^{\operatorname {RootOf}\left (-x \,{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z}^{2}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+c_{1} -{\mathrm e}^{\textit {\_Z}}\right )}\right ) {\mathrm e}^{-\operatorname {RootOf}\left (-x \,{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z}^{2}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+c_{1} -{\mathrm e}^{\textit {\_Z}}\right )} \]

✓ Solution by Mathematica

Time used: 0.299 (sec). Leaf size: 34

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

\[ \text {Solve}\left [x=\frac {e^{y(x)} (-y(x)-1)}{y(x)^2}+\frac {c_1 e^{2 y(x)}}{y(x)^2},y(x)\right ] \]