8.6.17 problem 17

Internal problem ID [787]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 17
Date solved : Monday, January 27, 2025 at 03:05:27 AM
CAS classification : [_exact]

\begin{align*} {\mathrm e}^{x}+{\mathrm e}^{y x} y+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

dsolve(exp(x)+exp(x*y(x))*y(x)+(exp(y(x))+exp(x*y(x))*x)*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ {\mathrm e}^{x y}+{\mathrm e}^{x}+{\mathrm e}^{y}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 20

DSolve[Exp[x]+Exp[x*y[x]]*y[x]+(Exp[y[x]]+Exp[x*y[x]]*x)*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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