67.4.36 problem Problem 6(a)

Internal problem ID [14080]
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)
Date solved : Tuesday, January 28, 2025 at 06:13:46 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} 10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} Q \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 10.160 (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)
 

\[ Q = \frac {\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-10 t +20}}{100}-\frac {\operatorname {Heaviside}\left (t -2\right )}{100}-\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-10 t +10}}{100}+\frac {\operatorname {Heaviside}\left (t -1\right )}{100} \]

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 50

DSolve[{10*D[ q[t],t]+100*q[t]==UnitStep[t-1]-UnitStep[t-2],{q[0]==0}},q[t],t,IncludeSingularSolutions -> True]
 

\[ q(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{100} e^{10-10 t} \left (-1+e^{10}\right ) & t>2 \\ \frac {1}{100} \left (1-e^{10-10 t}\right ) & 1<t\leq 2 \\ \end {array} \\ \end {array} \]