44.6.18 problem 18

Internal problem ID [7162]
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 : 18
Date solved : Sunday, March 30, 2025 at 11:49:34 AM
CAS classification : [_linear]

\begin{align*} \cos \left (x \right )^{2} \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{3} y&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

ode:=cos(x)^2*sin(x)*diff(y(x),x)+cos(x)^3*y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sec \left (x \right )+c_1 \csc \left (x \right ) \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 13

ode=Cos[x]^2*Sin[x]*D[y[x],x]+Cos[x]^3*y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sec (x)+c_1 \csc (x) \]

✓ Sympy. Time used: 1.073 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*cos(x)**3 + sin(x)*cos(x)**2*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} \tan ^{3}{\left (\frac {x}{2} \right )} - \frac {C_{1}}{\tan {\left (\frac {x}{2} \right )}} - \tan ^{2}{\left (\frac {x}{2} \right )} - 1}{\tan ^{2}{\left (\frac {x}{2} \right )} - 1} \]