1. ## ...A hard IVP?

Using V_i(t_i) = V_T

show that

P_ex = [(e^(t_i/RC) - 1 )P_app] / (e^(t_tot/RC) - 1)

2. Originally Posted by targus2
Using V_i(t_i) = V_T

show that

P_ex = [(e^(t_i/RC) - 1 )P_app] / (e^(t_tot/RC) - 1)
Sorry, but I have no idea what you are talking about here. In particular, I see no differential equation much less an initial value problem. I suspect you are talking about an electrical circuit problem but I have no idea what problem.

3. Eq 1: R(dV_i/dt) + (1/C)V_i + P_ex = P_app , 0 <= t <= t_i
Eq 2: R(dV_e/dt) + (1/C)V_e + P_ex = 0 , t_i <= t <= t_tot

A) Solve EQ 1 for V_i(t) with the initial condition V_i(0) = 0
B) Solve EQ 2 for V_e(t) with the initial condition V_e(t_i) = V_T
C) Using V_i(t_i) = V_T, show

P_ex = [((e^(t_i)/RC) - 1) * P_app] / ((e^(t_tot)/RC) - 1)

Knowns

V_i(0) = 0

V_e(t_i) = V_i(t_i) = V_T

V_e(tot) = 0

R, C, P_ex, P_app are constants

My solutions

A) V_i = C(P_app - P_ex)(1- (e^(t/RC)))

B) V_T = C(- P_ex)((e^(t/RC))-1)

C) ??

k This is the entire problem, does this help any??