74.3.29 problem 24

Internal problem ID [15889]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 08:17:26 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \tan \left (t \right )&=\sin \left (t \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 11

dsolve([diff(y(t),t)+y(t)*tan(t)=sin(t),y(0) = 0],y(t), singsol=all)
 

\[ y = -\cos \left (t \right ) \ln \left (\cos \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 12

DSolve[{D[y[t],t]+y[t]*Tan[t]==Sin[t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\cos (t) \log (\cos (t)) \]