Internal problem ID [10996]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 6(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {10 Q^{\prime }+100 Q-\operatorname {Heaviside}\left (-1+t \right )+\operatorname {Heaviside}\left (t -2\right )=0} \] With initial conditions \begin {align*} [Q \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
dsolve([10*diff(Q(t),t)+100*Q(t)=Heaviside(t-1)-Heaviside(t-2),Q(0) = 0],Q(t), singsol=all)
\[ Q \left (t \right ) = -\frac {\operatorname {Heaviside}\left (t -2\right )}{100}+\frac {\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-10 t +20}}{100}+\frac {\operatorname {Heaviside}\left (t -1\right )}{100}-\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-10 t +10}}{100} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 19
DSolve[{10*q'[t]+100*q[t]==UnitStep(t-1)-UnitStep(t-2),{q[0]==0}},q[t],t,IncludeSingularSolutions -> True]
\begin{align*} q(t)\to \frac {1}{100} \left (1-e^{-10 t}\right ) \text {UnitStep} \\ \end{align*}