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 : Tuesday, February 04, 2025 at 12:42:31 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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