Internal problem ID [137]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {{\mathrm e}^{x}+{\mathrm e}^{y x} y+\left ({\mathrm e}^{y}+{\mathrm e}^{y x} x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ {\mathrm e}^{x y \relax (x )}+{\mathrm e}^{x}+{\mathrm e}^{y \relax (x )}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.226 (sec). Leaf size: 20
DSolve[Exp[x]+Exp[x*y[x]]*y[x]+(Exp[y[x]]+Exp[x*y[x]]*x)*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^{y(x)}+e^{x y(x)}+e^x=c_1,y(x)\right ] \]