(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Please check my work on initial value problem. thank you!

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