Internal problem ID [2359]
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 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-2 y-\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve([diff(y(t),t)-2*y(t)=Heaviside(t-2)*exp(t-2),y(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = \left (-\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-t -2}+\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-4}+2\right ) {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 40
DSolve[{y'[t]-2*y[t]==UnitStep[t-2]*Exp[t-2],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} 2 e^{2 t} & t\leq 2 \\ e^{t-4} \left (-e^2+e^t+2 e^{t+4}\right ) & \text {True} \\ \\ \\ \\ \\ \end{align*}