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anonymous
 4 years ago
y"+6y'+9=0 can someone help me to explain this ODE?
anonymous
 4 years ago
y"+6y'+9=0 can someone help me to explain this ODE?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you can assume the solution is in the form of \[y=e^{\lambda x}\]then when you sub that in for y, you just need to solve for the lambda values.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so you get labda = 3 twice right, so y = \[e^{3x}\] + x*\[e^{3x}\] right?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Well, what you have in front of you is a very normal differential equation, I will assume you want the solution in R and not in C... So, here we go: The characteristic equation to this equation is \[r^2+6r+9=0 \] the discriminant is therefore \[\Delta=6^24*9=3636=0\] So we have one solution \[r=\frac{6}{2*9}=\frac{1}{3}\] and the canonical solution for a differential equation in real values with a characteristic equation with only one solution is, finally \[y:t \rightarrow (A*t+B)*e^{\frac{1}{3}*t} \] where A and B are constants determined by the initial conditions

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0r should be 6/(2*1) no?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh yes, small mistake... so you end up with r=3 instead, my bad
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