Assignment:
A circuit contains an electromotive force [E(t)], a capacitor with capacitance of C Farads, and a resistor with a resistance of R ohms. The voltage drop across the capacitor is Q/C where Q is the charge in Coulombs, so Kirchoff's Law gives
R * I + Q/C = E(t)
But I = dQ/dt, so
R * dQ/dt + 1/C * Q = E(t)
If the resistance (R) is 5 ohms, and the capacitance (C) is 0.05 Farads, and a battery gives a constant voltage of 60 V, then
5 * dQ/dt + 1/.05 * Q = 60 , or
dQ/dt + 4Q = 12
So here are my questions:
(a) Using Maple (I am using Maple 15), can you show me the commands to draw a direction field for this differential equation
(b)What is the limiting value of the charge
(c) Is there an equilibrium solution?
Provide complete and step by step solution for the question, use formulas.