Internal problem ID [143]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {{\mathrm e}^{y}+\cos \relax (x ) y+\left ({\mathrm e}^{y} x +\sin \relax (x )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 30
dsolve(exp(y(x))+cos(x)*y(x)+(exp(y(x))*x+sin(x))*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\LambertW \left (\frac {x \,{\mathrm e}^{-\frac {c_{1}}{\sin \relax (x )}}}{\sin \relax (x )}\right )-\frac {c_{1}}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 8.066 (sec). Leaf size: 25
DSolve[Exp[y[x]]+Cos[x]*y[x]+(Exp[y[x]]*x+Sin[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \csc (x)-\text {ProductLog}\left (x \csc (x) e^{c_1 \csc (x)}\right ) \\ \end{align*}