13.5 problem Problem 5

Internal problem ID [2334]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, class A]]

Solve \begin {gather*} \boxed {-y+y^{\prime }-6 \cos \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 17

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

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

Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 19

DSolve[{y'[t]-y[t]==6*Cos[t],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to 5 e^t+3 \sin (t)-3 \cos (t) \\ \end{align*}