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]
\[ \boxed {{\mathrm e}^{y}+\cos \left (x \right ) y+\left ({\mathrm e}^{y} x +\sin \left (x \right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = -\operatorname {LambertW}\left (\frac {x \,{\mathrm e}^{-\frac {c_{1}}{\sin \left (x \right )}}}{\sin \left (x \right )}\right )-\frac {c_{1}}{\sin \left (x \right )} \]
✓ Solution by Mathematica
Time used: 4.553 (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]
\[ y(x)\to c_1 \csc (x)-W\left (x \csc (x) e^{c_1 \csc (x)}\right ) \]