32.4.3 problem Recognizable Exact Differential equations. Integrating factors. Example 10.661, page 90

Internal problem ID [5814]
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. Example 10.661, page 90
Date solved : Monday, January 27, 2025 at 01:19:54 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 11.852 (sec). Leaf size: 16

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

\[ y(x)\to -\arcsin \left (e^x (x+c_1)\right ) \]