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anonymous
 5 years ago
Use the method of undetermined coefficients to find one solution of:
y'' + 2y'  5y = (1t^2 + 8t 4)*exp(4t)
Note that the method finds a specific solution, not the general one.
y =?
anonymous
 5 years ago
Use the method of undetermined coefficients to find one solution of: y'' + 2y'  5y = (1t^2 + 8t 4)*exp(4t) Note that the method finds a specific solution, not the general one. y =?

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apples
 5 years ago
Best ResponseYou've already chosen the best response.0For this, you'll want your guess to be the product of the two separate guesses. \[Ae^{4t} (Bt^2+Ct+D)\]

apples
 5 years ago
Best ResponseYou've already chosen the best response.0After plugging in the guess, gather the coefficients together and solve.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks again. I appreciate it. Differential equations is just not my cup of tea. I wonder how that relates to Chemistry major though...

apples
 5 years ago
Best ResponseYou've already chosen the best response.0By the way, the expansion for that problem is (as I'm sure you've already seen) quite a monster, so I didn't particularly want to type it out here unless needed. I don't know much about Chemistry, but I do know that differential equations are important for things like the heat equation (which may have applications in Chemistry, I'm not sure).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I know. That's the impression I get from taking Physics (for Physics majors not engineers). My school has separate Physics classes for Biology, Chemistry/Physics/Geological Science majors, and one specifically for Engineers. I'm working out the problem right now and it's becoming really messay. Thanks again.

apples
 5 years ago
Best ResponseYou've already chosen the best response.0A hint to make this easier: You can ignore the exponential, find the particular solution for t^2 + 8t  4, and then multiply that with the exponential.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks for the hint. I tried expanding it and plugging it back into the equation. I think my arithmetic may be wrong since I got: A = 32, B = 1/32, C = 1/4 and D = 1/8.

apples
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, I definitely got something different. When solving \[y'' + 2y'  5y = t^2 + 8t  4\] I got \[2A + 4At + 2b  5At^2  5Bt  5C = t^2 + 8t  4\] and thus the system of equations \[\begin{align*}2A + 2B  5C &= 4 \\ 4A  5B &= 8 \\ 5A &= 1\end{align*}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0differential equations is probably one of the most useful maths in sciences

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hmm, I figured it was: y =\[A \exp(4t)(Bt ^{2} + Ct + D)\] I then took the 1st and 2nd derivative of that to plug into: y'' + 2y''  5y = exp(4t)(t^(2) + 8t 4). I think that's why our answers are different.

apples
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, yeah. I used the hint I gave to make life a bit easier for myself. :) As long as it works when you plug it in, you should be fine.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0When I did that and entered into webwork (online HW), my answer was wrong so I'll try your method and see what happens.

apples
 5 years ago
Best ResponseYou've already chosen the best response.0Just make sure you multiply my particular solution by e^(4t) after finding it
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