Internal problem ID [2867]
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`]]
\[ \boxed {y^{\prime }+2 y=2 \operatorname {Heaviside}\left (t -1\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 2.328 (sec). Leaf size: 24
dsolve([diff(y(t),t)+2*y(t)=2*Heaviside(t-1),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = -\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-2 t +2}+\operatorname {Heaviside}\left (t -1\right )+{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 26
DSolve[{y'[t]-y[t]==2*UnitStep[t-1],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} e^t & t\leq 1 \\ -2+2 e^{t-1}+e^t & \text {True} \\ \end {array} \\ \end {array} \]