Internal problem ID [2617]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {y^{2} {\mathrm e}^{y x}+\cos \relax (x )+\left ({\mathrm e}^{y x}+x y \,{\mathrm e}^{y x}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 16
dsolve((y(x)^2*exp(x*y(x))+cos(x))+(exp(x*y(x))+x*y(x)*exp(x*y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\LambertW \left (-x \left (c_{1}+\sin \relax (x )\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 89.129 (sec). Leaf size: 19
DSolve[(y[x]^2*Exp[x*y[x]]+Cos[x])+(Exp[x*y[x]]+x*y[x]*Exp[x*y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\text {ProductLog}(x (-\sin (x)+c_1))}{x} \\ \end{align*}