38.6.17 problem 17

Internal problem ID [8447]
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 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 05:37:03 PM
CAS classification : [_linear]

\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \end{align*}

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

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

\[ y = \cos \left (x \right ) c_1 +\sin \left (x \right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to \sin (x)+c_1 \cos (x) \end{align*}

✓ Sympy. Time used: 0.427 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*sin(x) + cos(x)*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \cos {\left (x \right )} + \sin {\left (x \right )} \]