20.21.5 problem Problem 5

Internal problem ID [3932]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 5
Date solved : Monday, January 27, 2025 at 08:04:42 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=6 \cos \left (t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 2.685 (sec). Leaf size: 17

dsolve([diff(y(t),t)-y(t)=6*cos(t),y(0) = 2],y(t), singsol=all)
 

\[ y = -3 \cos \left (t \right )+3 \sin \left (t \right )+5 \,{\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 19

DSolve[{D[y[t],t]-y[t]==6*Cos[t],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 5 e^t+3 \sin (t)-3 \cos (t) \]