Exercise $5\mathrm{.}3\mathrm{.}10$ Consider an RC circuit like that shown in shown in Figure $2\mathrm{.}2,$ with resistor $R=10$ ohms and capacitor $C={10}^{-4}F.$ The capacitor is uncharged at time $t=0.$ Suppose the voltage source is $V(t)=2$ volts for time $0t0\mathrm{.}003$ seconds and then switches to $V(t)=5$ volts for $t>0\mathrm{.}003.$ Formulate an appropriate ODE for the charge $q(t)$ on the capacitor, withlinitial condition, and solve using the Laplace transform. Plot the solution on the interval $0t0\mathrm{.}01.$

Use equation Rq$\text{'}($t$)+$q$($t$)/$C $=$ V$($t$)$