anonymous
  • anonymous
y"+6y'+9=0 can someone help me to explain this ODE?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
you 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
  • anonymous
so you get labda = -3 twice right, so y = \[e^{-3x}\] + x*\[e^{-3x}\] right?
anonymous
  • anonymous
Well, 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 \[\Delta=6^2-4*9=36-36=0\] 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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
r should be -6/(2*1) no?
anonymous
  • anonymous
not (2*9)?
anonymous
  • anonymous
oh yes, small mistake... so you end up with r=-3 instead, my bad
anonymous
  • anonymous
great thanks :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.