32.4.13 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.5, page 90

Internal problem ID [5824]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Exercise 10.5, page 90
Date solved : Monday, January 27, 2025 at 01:20:04 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 18

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

\[ {\mathrm e}^{x} \sin \left (y \left (x \right )\right )+x \,{\mathrm e}^{-y \left (x \right )}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.368 (sec). Leaf size: 24

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

\[ \text {Solve}\left [x \left (-e^{-y(x)}\right )-e^x \sin (y(x))=c_1,y(x)\right ] \]