- #1
DmytriE
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Homework Statement
Consider the first order differential equation
[itex]\frac{dx(t)}{dt} + ax(t) = f(t), x(0) = x_{0}, t\geq0[/itex]
Suppose the "input signal" [itex] f(t)=e^{-t}, t\geq0 [/itex]. (a) Find the solution to the equation. Find a condition on the parameter a so that the solution of the (forced) system approaches zero as t→∞.
Homework Equations
[itex]\frac{dy}{dt} + p(x)y = 0 [/itex]
The Attempt at a Solution
Setup as a homogenous equation therefore f(t) = 0.
[itex]\frac{dx(t)}{dt} + ax(t) = 0 [/itex]
[itex]\frac{dx(t)}{x(t)} = -a*dt [/itex]
[itex] ln(x(t)) = -at [/itex]
[itex] x(t) = e^{-at} [/itex]
I don't know how to proceed any further...