- #1
darryw
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Homework Statement
Solve the following initial value problem. Sketch the solution and describe its behavior
as t increases.
y'' + 4y' + 3y = 0
y(0) = 2
y'(0) = -1
1st i solved the characteristic:
r^2 + 4r + 3 = 0
r = -1
r = -3
then the general solution is;
y = c_1e^-x + c_2e^-3x
also..
y' = -c_1e^-x - 3c_2e^-3x
so after i plug in the initial values i get 2 equations and 2 unknowns..
c_1 + c_2 = 2
-c_1 - 3c_2 = -1
c_1 = 5/2
c_2 = -1/2
so the solution with initial conditions (is this called "particular solution?) is:
y = (5/2)e^-x - (1/2)e^-3x
is this much correct before i describe the equations behavior? thanks alot