7.3.3 problem 3

Internal problem ID [43]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 3
Date solved : Saturday, March 29, 2025 at 04:27:19 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

ode:=diff(y(x),x) = y(x)*sin(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.248 (sec). Leaf size: 8

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

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