Differential equation word problem help please. Thank you very much?

2016-05-26 2:08 am
Consider a series circuit consisting of a resistor of R ohms, an inductor of L henries, and variable voltage source of V(t) volts (time t in seconds). The current through the circuit I(t) (in amperes) satisfies the differential equation:

dI/dt + (R/L)*I= (1/L)*V(t)

Find the solution to this equation with the initial condition I(0) = 0, assuming that R= 80 Ω , L=5 H, and V(t) is constant with V(t)= 10

回答 (1)

2016-05-26 11:43 am
✔ 最佳答案
dI/dt + (80/5)*I = (1/5)*10
dI/dt + 16I = 2
dI/dt = - 16I + 2
dI = ( - 16I + 2 ) dt
I = ∫ ( - 16I + 2 ) dt = - 8I^2 + 2I + C

Substitute into I(0) = 0 , we have
I(0) = C = 0
Hence,
I(t) = - 8I^2 + 2I ..... Ans


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