Internal problem ID [3985]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 744.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+y \,{\mathrm e}^{x}+{\mathrm e}^{y}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 31
dsolve((exp(x)+x*exp(y(x)))*diff(y(x),x)+y(x)*exp(x)+exp(y(x)) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\left (\operatorname {LambertW}\left (x \,{\mathrm e}^{-x} {\mathrm e}^{-c_{1} {\mathrm e}^{-x}}\right ) {\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 3.489 (sec). Leaf size: 33
DSolve[(Exp[x]+x Exp[y[x]])y'[x]+y[x] Exp[x]+Exp[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-x}-W\left (x e^{-x+c_1 e^{-x}}\right ) \]