Economics Dynamics Problems 55

Economics Dynamics Problems 55 - Continuous dynamic systems...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Continuous dynamic systems 39 Furthermore, if we have the initial condition that y (0) = y 0 , then we can solve for c y 0 =− a b + c c = y 0 + a b Hence, we have the solution to the initial value problem of y ( t ) a b + ± y 0 + a b ² e bt Example 2.11 Suppose we have the initial value problem dy dt = 2 y + 4 ty (0) = 1 Applying the four-step procedure we have Step 1 2 y = 4 t Step 2 µ ( t ) = e ³ 2 = e 2 t Step 3 e 2 t y = ´ 4 te 2 t + c Step 4 e 2 t y 2 te 2 t e 2 t + c Or y 2 t 1 + ce 2 t Since y (0) = 1, then 1 1 + c c = 2 Hence, y ( t ) 2 t 1 + 2 e 2 t 2.3 Compound interest If an amount A is compounded annually at a market interest rate of
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

Ask a homework question - tutors are online