A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality k > 0. (a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Your answer will contain the unknown constants r and k. Q' = r-kQ (b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain r and k. = 7/1 (1 - e-kt) (c) What is the limiting long-run value of Q? lim Q(t) t→∞0 = r k

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Q: express L−1[F(s)G(s)] in terms of a convolution integral.

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Q: solve the given initial-value problem. Q. y′′+3y′+2y =12te2t, y(0)=0, y′(0)=1.

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Q: Find the solution of Non linear higher order partial differential equation…

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