74.5.3 problem 3

Internal problem ID [15967]
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 : 3
Date solved : Tuesday, January 28, 2025 at 08:25:02 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(t),t)-y(t)=2*cos(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 30

DSolve[D[y[t],t]-y[t]==2*Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (\int _1^t2 e^{-K[1]} \cos (K[1])dK[1]+c_1\right ) \]