Internal problem ID [2566]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {{\mathrm e}^{y} y^{\prime }+2 x -2 \,{\mathrm e}^{y} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve(exp(y(x))*diff(y(x),x)+2*x=2*x*exp(y(x)),y(x), singsol=all)
\[ y \relax (x ) = -\ln \left (-\frac {1}{-1+{\mathrm e}^{x^{2}} c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 1.985 (sec). Leaf size: 21
DSolve[Exp[y[x]]*y'[x]+2*x==2*x*Exp[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (1+e^{x^2+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}