Internal problem ID [2545]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{y} \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(y(x),x)=exp(y(x))*sin(x),y(x), singsol=all)
\[ y \relax (x ) = -\ln \left (\cos \relax (x )-c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.345 (sec). Leaf size: 15
DSolve[y'[x]==Exp[y[x]]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\log (\cos (x)-c_1) \\ \end{align*}