Internal problem ID [12323]
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`]]
\[ \boxed {y^{\prime }+y=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-2+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 5.203 (sec). Leaf size: 22
dsolve([diff(y(t),t)+y(t)=Heaviside(t)-Heaviside(t-2),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = 1-\operatorname {Heaviside}\left (t -2\right )+\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{2-t} \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 31
DSolve[{y'[t]+y[t]==UnitStep[t]-UnitStep[t-2],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 1 & 0\leq t\leq 2 \\ e^{2-t} & t>2 \\ e^{-t} & \text {True} \\ \end {array} \\ \end {array} \]