Internal problem ID [11527]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 3, Laplace transform. Section 3.2.1 Initial value problems. Exercises page
156
Problem number: 6(j).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {-2 x+x^{\prime }=\operatorname {Heaviside}\left (t -1\right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(x(t),t)=2*x(t)+Heaviside(t-1),x(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\operatorname {Heaviside}\left (t -1\right ) \left (-1+{\mathrm e}^{2 t -2}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 25
DSolve[{x'[t]==2*x[t]+UnitStep[t-1],{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{2} \left (-1+e^{2 t-2}\right ) & t>1 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]