25.1.3 problem 3

Internal problem ID [4215]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 3
Date solved : Monday, January 27, 2025 at 08:42:35 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)=exp(y(x))*sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\ln \left (\cos \left (x \right )-c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.283 (sec). Leaf size: 15

DSolve[D[y[x],x]==Exp[y[x]]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\log (\cos (x)-c_1) \]