74.11.51 problem 62 (b)

Internal problem ID [16301]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 62 (b)
Date solved : Tuesday, January 28, 2025 at 09:02:08 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 23

dsolve([diff(y(t),t)+y(t)=cos(2*t),y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {\cos \left (2 t \right )}{5}+\frac {2 \sin \left (2 t \right )}{5}-\frac {{\mathrm e}^{-t}}{5} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 28

DSolve[{D[y[t],t]+y[t]==Cos[2*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \int _0^te^{K[1]} \cos (2 K[1])dK[1] \]