Internal problem ID [3962]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {{\mathrm e}^{x}-\sin \relax (y)+\cos \relax (y) y^{\prime }=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = -\arcsin \left (\left (c_{1}+x \right ) {\mathrm e}^{x}\right ) \]
✓ Solution by Mathematica
Time used: 3.221 (sec). Leaf size: 16
DSolve[(Exp[x]-Sin[y[x]])+Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcSin}\left (e^x (x+c_1)\right ) \\ \end{align*}