Internal problem ID [4418]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(1/y(x)*diff(y(x),x)+y(x)*exp(cos(x))*sin(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{{\mathrm e}^{\cos \left (x \right )}-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.3 (sec). Leaf size: 21
DSolve[1/y[x]*y'[x]+y[x]*Exp[Cos[x]]*Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{e^{\cos (x)}+c_1} \\ y(x)\to 0 \\ \end{align*}