67.1.4 problem Problem 1(d)

Internal problem ID [13951]
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)
Date solved : Tuesday, January 28, 2025 at 06:09:29 AM
CAS classification : [_separable]

\begin{align*} x \left ({\mathrm e}^{y}+4\right )&={\mathrm e}^{x +y} y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.186 (sec). Leaf size: 19

dsolve(x*(exp(y(x))+4)=exp(x+y(x))*diff(y(x),x),y(x), singsol=all)
 

\[ y = \ln \left (-4+c_{1} {\mathrm e}^{-\left (x +1\right ) {\mathrm e}^{-x}}\right ) \]

✓ Solution by Mathematica

Time used: 4.113 (sec). Leaf size: 51

DSolve[x*(Exp[y[x]]+4)==Exp[x+y[x]]*D[y[x],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*}