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`]]
\[ \boxed {2 y+y^{\prime }-2 \operatorname {Heaviside}\left (t -1\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 25
dsolve([diff(y(t),t)+2*y(t)=2*Heaviside(t-1),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-2 t +2}+{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.044 (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*}