Find a particular solution satisfying the initial condition

Reference no: EM131012572

A hospital patient is receiving pain medication through an IV. The drug enters the patient's bloodstream at a constant rate r. The rate at which the drug leaves the bloodstream is proportinal to the amount of drug present. Let t represent time (measured in minutes) and let y(t) represent the amount of the drug in the bloodstream at time t.

(a) Determine the first-order ODE that models this situation.

(b) Rewrite the ODE to show tht it is linear, and state whether it is homogeneous or non-homogeneous.

(d) Solve to find a one-parameter family of solutions.

(e) Find a particular solution satisfying the initial condition y(0)=0.

Reference no: EM131012572

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