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 : Sunday, March 30, 2025 at 10:48:01 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = \frac {1}{-{\mathrm e}^{\cos \left (x \right )}+c_1} \]

✓ Mathematica. Time used: 0.29 (sec). Leaf size: 21

ode=1/y[x]*D[y[x],x]+y[x]*Exp[Cos[x]]*Sin[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{e^{\cos (x)}+c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.293 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*exp(cos(x))*sin(x) + Derivative(y(x), x)/y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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