8.6.23 problem 23

Internal problem ID [793]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 23
Date solved : Monday, January 27, 2025 at 03:07:12 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: 0.016 (sec). Leaf size: 23

dsolve(exp(y(x))+cos(x)*y(x)+(exp(y(x))*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: 3.644 (sec). Leaf size: 25

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

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