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Differential Equations Quiz Solutions by Hanan Abdisubhan is a document available to read on EtoBox.

1) The differential equation is dx/dt = kx - x^3. If k ≤ 0, x = 0 is the only critical point and it is stable. If k > 0, the critical points are x = 0, ±√k. x = 0 is unstable, and x = ±√k are stable. 2) The rate of change of the alligator population P is proportional to P^2. Using initial conditions, the equation is derived as dP/dt = kP^2 - P - 1/12 = 1/240t. This shows the population will be 48 when t = 20 years. The population will continue increasing indefinitely.

Author

Hanan Abdisubhan

Language

EN