1) Find the equilibrium solution of the differential equation:
Dy/dt = 3y(1-(1/2)y)
Sketch the slope field and use it to determine whether each equilibrium is stable or unstable.
2) Consider the initial value problem
Y^1 = 4 - y^2, y(0) = 1
Use the Euler's method with 5 steps to estimate y(1). Sketch the field and use it to determine whether the estimate is an overestimate or an underestimate.
3) Find the Taylor polynomial of degree 4 as an approximation of the Solution of the initial problem.
Y^1 - 2x^2 + y^2 = 0, y (0) = 2© BrainMass Inc. brainmass.com October 25, 2018, 9:50 am ad1c9bdddf
This solutions includes step by step solutions to questions on equilibrium solutions, Euler's solutions and Taylor polynomial of degree 4 for a differential equation.
Applying Differential Equations and Logistic Equations
The number of bacteria in a Petri dish was initially determined to be 200. After one hour, the number had increased to 500 and after another hour to 1,000. Assume that the rate of bacterial growth in the dish at any time t can be calculated using the logistic equation dB/dt = B(a-bB), which I know to use the formula B = aBo/(bBo+(a - bBo)e^(-at))).View Full Posting Details