題組內容

3. Consider the differential equation governing the pressure \( p \) is \( \dot{Q}(t) = C \frac{dp}{dt} + \frac{p}{R} \), where \( C \) and \( R \) are arbitrary constants, \( \dot{Q}(t) \) is the flow rate, and \( t \) is time.

(b) If the flow rate is \( \dot{Q}(t) = \frac{t}{R} \), solve the equation in part (a). (10%)