Internal problem ID [2696]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {y-\left ({\mathrm e}^{y}+2 y x -2 x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 62
dsolve(y(x)=(exp(y(x))+2*x*y(x)-2*x)*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (\textit {\_Z}^{2} x -c_{1}+\textit {\_Z} +{\mathrm e}^{\RootOf \left (-x \,{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z}^{2}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+c_{1}-{\mathrm e}^{\textit {\_Z}}\right )}\right ) {\mathrm e}^{-\RootOf \left (-x \,{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z}^{2}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+c_{1}-{\mathrm e}^{\textit {\_Z}}\right )} \]
✓ Solution by Mathematica
Time used: 0.297 (sec). Leaf size: 34
DSolve[y[x]==(Exp[y[x]]+2*x*y[x]-2*x)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {e^{y(x)} (-y(x)-1)}{y(x)^2}+\frac {c_1 e^{2 y(x)}}{y(x)^2},y(x)\right ] \]