Internal problem ID [12344]
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`]]
\[ \boxed {10 Q^{\prime }+100 Q=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right )} \] With initial conditions \begin {align*} [Q \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 5.094 (sec). Leaf size: 37
dsolve([10*diff(Q(t),t)+100*Q(t)=Heaviside(t-1)-Heaviside(t-2),Q(0) = 0],Q(t), singsol=all)
\[ Q \left (t \right ) = \frac {\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-10 t +20}}{100}-\frac {\operatorname {Heaviside}\left (t -2\right )}{100}-\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-10 t +10}}{100}+\frac {\operatorname {Heaviside}\left (t -1\right )}{100} \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 50
DSolve[{10*q'[t]+100*q[t]==UnitStep[t-1]-UnitStep[t-2],{q[0]==0}},q[t],t,IncludeSingularSolutions -> True]
\[ q(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{100} e^{10-10 t} \left (-1+e^{10}\right ) & t>2 \\ \frac {1}{100} \left (1-e^{10-10 t}\right ) & 1<t\leq 2 \\ \end {array} \\ \end {array} \]