74.5.47 problem 54

Internal problem ID [16011]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 54
Date solved : Tuesday, January 28, 2025 at 08:26:27 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y&=8 \cos \left (4 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(t),t)+4*y(t)=8*cos(4*t),y(t), singsol=all)
 

\[ y = \sin \left (4 t \right )+\cos \left (4 t \right )+{\mathrm e}^{-4 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 34

DSolve[D[y[t],t]+4*y[t]==8*Cos[4*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (\int _1^t8 e^{4 K[1]} \cos (4 K[1])dK[1]+c_1\right ) \]