Solve the following linear systems of differential equations.

A hamster receives a dose of 3 mg. of a compound and then 2/3 as much as the previous dose at the end of every hour. What is the maximum amount of the compound it will receive?   (Solve using Differential Equations)

Consider the non-linear system of differential equations, x₁ = x₁(x₂ − 1), x2 = − x₂(x₁ -X2(x1 + 1).

Find a differential equation whose general solution is y = c₁e²t + c2e2t.

A pan of boiling water with a temperature of 212°F is set in a bin of ice with a temperature of 32°F. The pan cools to 65°F in 33 minutes. (a) Find To, D, and a so that T(t) = T₁ + Dat models the data, where t is in hours. (b) Find the temperature of the pan after 15 minutes. (c) How long did it take the pan to reach 35°F? Support your result graphically. (a) To (Round to the nearest integer as needed.) =

Solve the following system of differential equations: r(t) = 4x₁(t) = x₂(t); x₂(t) = − x₁(t) + 3x2(t) + x3(t); x3 (t) = 3x₁ (t) — 2x2(t) + 2x3(t). with initial conditions x₁(0) = x₂(0) = x3 (0) = 1.

The windchill index announced during the winter by the weather bureau measures how cold it "feels" for a given temperature t (in degrees Fahrenheit) and wind speed w (in miles per hour). It is calculated by the formula C(t, w) = 35.74 + 0.6215t - 35.75w 0.16 + 0.4275tw0.16 + '.+ If the temperature is 31 degrees and the wind speed is 10 miles per hour, estimate the change in the windchill temperature if the wind speed increases by 4 miles per hour and the temperature drops by 5 degrees. (Round your answer to two decimal places.)

In 1993, the moose population in a park was measured to be 3200. By 1996, the population was measured again to be 2100. If the population continues to change linearly: Find a formula for yhe moose pupulation, P,in terms of t, the years since 1990. P(t)= what does your model predict the moose population to be in 2009?

Find the most general real-valued solution to the linear system of differential equations 12/2 x₁(t) x₂(t) = ] = C1 -21 x. + C₂