Internal problem ID [11895]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 2, First Order Equations. Problems page 149
Problem number: Problem 1(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \left ({\mathrm e}^{y}+4\right )-{\mathrm e}^{x +y} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
dsolve(x*(exp(y(x))+4)=exp(x+y(x))*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (-4+c_{1} {\mathrm e}^{-x \,{\mathrm e}^{-x}-{\mathrm e}^{-x}}\right ) \]
✓ Solution by Mathematica
Time used: 4.746 (sec). Leaf size: 51
DSolve[x*(Exp[y[x]]+4)==Exp[x+y[x]]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (-4+e^{e^{-x} \left (-x+c_1 e^x-1\right )}\right ) y(x)\to \log (4)+i \pi y(x)\to \log (4)+i \pi \end{align*}