Question

Suppose R = 10, C = .02, Q(0) = 0, E(t) = 100e^-5t. Find Q(t) and I(t).

Answer 1

R(dQ/dt) + (1/C)*Q = E(t)
10Q' + 50Q = 100e^-5t

Answer 2

10(Q' + 5Q) = 100e^-5t -> Q' + 5Q = 10e^-5t

Answer 3

solve the homogenous first

Answer 4

10Q' + 50Q = 100e^-5t

Q' + 5Q = 10e^-5t

Q' + 5Q = 0

Q' =-5Q

Q'/Q = -5

ln(Q) = -5t + C

Q = Ce^-5t

Answer 5

then solve the particular

Answer 6

Q = (C + 10t) e^-5t

Q(0) = 0

0 = (C + 0) 1

Q = 10t e^-5t

maybe .....

Answer 7

Wait. Why is the particular Q = (C + 10t)e^-5t?