44.5.1 problem 1

Internal problem ID [7063]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 1
Date solved : Wednesday, March 05, 2025 at 04:04:57 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sin \left (5 x \right ) \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 12

ode:=diff(y(x),x) = sin(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\cos \left (5 x \right )}{5}+c_{1} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 16

ode=D[y[x],x]==Sin[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {1}{5} \cos (5 x)+c_1 \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(5*x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} - \frac {\cos {\left (5 x \right )}}{5} \]