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(a) Find the charge on the capacitor at any time.

This is linear so i found the integrating factor which is (20+t)^5

and solved q(20+t)^5 = 20 integral ((20+t)^4) dt

and got q(20+t)^5 = 4((20+t)^5) + C

my C value i got was -9600000

solving for q gave me q = 4 - ((9600000)/((20+t)^5))

(b) Transient and steady state solution

Transient = - ((9600000)/((20+t)^5))

Steady state = 4

(c) Find the current in the circuit at any time, hence the maximum current in the circuit.

current = i = dq/dt

I differentiated and got dq/dt = 48000000((20+t)^-6)

**My problems

Firstly does everything follow, is my logic correct?

Secondly for the maximum current that occurs at t = 0 (presuming my equations are correct) is there anyway of showing working for that, other then stating its at t = 0? (t = 0, i = .75)