Internal problem ID [2868]
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`]]
\[ \boxed {y^{\prime }-2 y=\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 2.297 (sec). Leaf size: 43
dsolve([diff(y(t),t)-2*y(t)=Heaviside(t-2)*exp(t-2),y(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = -\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}+\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-4+2 t}+2 \,{\mathrm e}^{2 t} \]
✓ 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]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 2 e^{2 t} & t\leq 2 \\ e^{t-4} \left (-e^2+e^t+2 e^{t+4}\right ) & \text {True} \\ \end {array} \\ \end {array} \]