STM 2100 Quiz April 2 2020 Consider the radioactive decay model dy/dt = -0.1y y(0) =...

STM 2100 Quiz April 2 2020

Consider the radioactive decay model

dy/dt = -0.1y

y(0) = 10

a. Use separation of variables to solve the ODE

b. At what time does y(t) = 5?

2. Consider the logistic model given by the following ODE

dy/dt = y(1-y)

y(0) = 0.1

a. Use separation of variables to rewrite the problem as an equality of two integrals

b. Use partial fractions to rewrite 1/y(1-y) as the sum of two fractions, each of which has a single factor in its denominator

c. Substitute your result for (b) into (a), and solve for y(t)

d. At what time does y(t) = 0.2? At what time does y(t) = 0.4?

Expert Solution

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milcah answered 2 years ago

Use a LaPlace transform to solve d^2x/dt^2+dx/dt+dy/dt=0 d^2y/dt^2+dy/dt-4dy/dt=0 x(0)=1,x'(0)=0 y(0)=-1,y'(0)=5

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