Internal problem ID [11519]
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: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {-x+x^{\prime }=-2 \operatorname {Heaviside}\left (t -1\right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 5.11 (sec). Leaf size: 27
dsolve([diff(x(t),t)=x(t)-2*Heaviside(t-1),x(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \left (-2 \,{\mathrm e}^{t -1}+2\right ) \operatorname {Heaviside}\left (t -1\right )+{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 26
DSolve[{x'[t]==x[t]-2*UnitStep[t-1],{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \begin {array}{cc} \{ & \begin {array}{cc} e^t & t\leq 1 \\ 2-2 e^{t-1}+e^t & \text {True} \\ \end {array} \\ \end {array} \]