44.6.36 problem 36

Internal problem ID [7180]
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 : 36
Date solved : Tuesday, February 04, 2025 at 12:44:53 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 11

dsolve([diff(y(x),x)+tan(x)*y(x)=cos(x)^2,y(0) = -1],y(x), singsol=all)
 

\[ y = \cos \left (x \right ) \left (\sin \left (x \right )-1\right ) \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 12

DSolve[{D[y[x],x]+Tan[x]*y[x]==Cos[x]^2,{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (\sin (x)-1) \cos (x) \]