36.1.16 problem 16

Internal problem ID [6271]
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
Date solved : Monday, January 27, 2025 at 01:52:35 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve(1/y(x)*diff(y(x),x)+y(x)*exp(cos(x))*sin(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.290 (sec). Leaf size: 21

DSolve[1/y[x]*D[y[x],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*}