7.7.23 problem 23

Internal problem ID [201]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:40:50 AM
CAS classification : [_exact]

\begin{align*} {\mathrm e}^{y}+y \cos \left (x \right )+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 23

dsolve(exp(y(x))+y(x)*cos(x)+(x*exp(y(x))+sin(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\operatorname {LambertW}\left (\csc \left (x \right ) {\mathrm e}^{-\csc \left (x \right ) c_1} x \right )-\csc \left (x \right ) c_1 \]

✓ Solution by Mathematica

Time used: 4.590 (sec). Leaf size: 25

DSolve[Exp[y[x]]+y[x]*Cos[x]+(x*Exp[y[x]]+Sin[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \csc (x)-W\left (x \csc (x) e^{c_1 \csc (x)}\right ) \]