Internal problem ID [10975]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 3(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y-\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -2\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve([diff(y(t),t)+y(t)=Heaviside(t)-Heaviside(t-2),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )+\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-t +2}-{\mathrm e}^{-t} \operatorname {Heaviside}\left (t \right )+{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 31
DSolve[{y'[t]+y[t]==UnitStep[t]-UnitStep[t-2],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} 1 & 0\leq t\leq 2 \\ e^{2-t} & t>2 \\ e^{-t} & \text {True} \\ \\ \\ \\ \\ \end{align*}