Internal problem ID [11518]
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(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {x^{\prime }+5 x=\operatorname {Heaviside}\left (-2+t \right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve([diff(x(t),t)+5*x(t)=Heaviside(t-2),x(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\operatorname {Heaviside}\left (t -2\right )}{5}-\frac {\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-5 t +10}}{5}+{\mathrm e}^{-5 t} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 37
DSolve[{x'[t]+5*x[t]==UnitStep[t-2],{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \begin {array}{cc} \{ & \begin {array}{cc} e^{-5 t} & t\leq 2 \\ \frac {1}{5} e^{-5 t} \left (5-e^{10}+e^{5 t}\right ) & \text {True} \\ \end {array} \\ \end {array} \]