Internal problem ID [2358]
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 10.7.
page 704
Problem number: Problem 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+2 y-2 \theta \left (t -1\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve([diff(y(t),t)+2*y(t)=2*Heaviside(t-1),y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \left (-{\mathrm e}^{-2 t +2}+1\right ) \theta \left (t -1\right )+{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 25
DSolve[{y'[t]-y[t]==2*UnitStep[t-1],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} e^t & t\leq 1 \\ -2+e^{t-1} (2+e) & \text {True} \\ \\ \\ \\ \\ \end{align*}