Response to the following Differential Equation Questions:
Use separation of variables to solve to the ODE:
N ?=?{k?_+-k_- ln??(N)}N?;k_+,k_- and t>0;N(0)= N_0>0.
Hint: Use u = ln(N) for u-substitution.
Substitute your solution into the differential equation and show that it is in fact the solution.
Evaluate your solution for N(t) as t→∞ .
For what values of N will N ?=0?
For what values of N_0 will
N ?(0)>0
b) N ?(0)<0
Considering your answers to questions 3), 4) and 5), describe how N and N ? change from t=0 to t →∞ for cases a) and b) in question 5).
Use separation of variables to solve to the ODE: dx/dt= α_1 x-α_2 x^2;t>0;x(0)= x_0>0
You may use integral tables.
Find the equilibrium points of the ODE.
Evaluate the solution as t→∞
What conclusions can you make relative to the answers to questions 2 and 3.