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lilMissMindset
Group Title
(D^2 + 9)y =5e^x  162x
i need to check if my answer is right.
 2 years ago
 2 years ago
lilMissMindset Group Title
(D^2 + 9)y =5e^x  162x i need to check if my answer is right.
 2 years ago
 2 years ago

This Question is Closed

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
@AnimalAin this.
 2 years ago

partyrainbow276 Group TitleBest ResponseYou've already chosen the best response.0
Awesome! u did it write
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
this is my answer: 2Ae^x + B + Cx = 5e^x 162x
 2 years ago

partyrainbow276 Group TitleBest ResponseYou've already chosen the best response.0
lets see...... AWESOME AWESOME :) thats right good job
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
It's been a minute since I've done these, but I think the way is to consider the homogeneous solution by using an auxilliary (sp?) equation, then fit a particular solution that will match the RHS.
 2 years ago

partyrainbow276 Group TitleBest ResponseYou've already chosen the best response.0
lilmissmindset is right thats what i got for my answer
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
That's the problem we did before.....
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
yes yes, this is the first question i asked. it's just that the book says the general solution for this is \[=C _{1} \cos 3x+ C _{2} \sin3x + \frac{ 1 }{ 2 } e ^{x} 18xy \]
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
there's no y after 18x SORRY
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
Lets look at this in more detail.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
and our answer is 5/2 e^x 162x
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
i thought, maybe there's something wrong with me, getting the solution after all
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
\[(D^2 + 9)y =5e^x  162x\]Consider\[(D^2 + 9)y =0\]Aux equation\[r^2+9=0 \implies r= \pm 3i \implies y _{h}=C _{1} \cos 3x +C_2 \sin3x\]OK so far?
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
yeps. ok.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
ok with that part,
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
Then we find the particular solution. Consider the first part of the RHS by itself, so\[(D^2 + 9)y_p =5e^x \implies y_p=\frac{e^x}{2}\]
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
This is true since the derivative of the e^x term is always itself. That means the second derivative is the same as the original function. Added to the nine copies of the original function, we get 10ysubp=5e^x.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
owwww. i understand,
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
Now consider the polynomial part. The second derivative of a linear function is zero, so we get\[ 9y_{p2} = 162x \implies y_{p2} =19x\]
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
So we get something like\[y=y_h+y_p=C_1\cos 3x+C_2\sin3x+\frac{e^x}{2}19x\]
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
i forgot to multiply \[y _{p}\] with 9 when i substitute, right? that's why i did ot get the answer,
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
not*
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
Actually, my division is horrible today.... should be 18 in the last term; exactly as your text had said.
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
I hope you've got this; you're wearing me out....LOL
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
actually, it's the same for the two of us. LOL hey, thanks a lot. you've been helping me large. Sorry for the stress,
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
SORRY!
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
i get it, i'm just confused on some parts.
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
No stress. It's fun working with students that work hard and get it. Do math every day.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
i'll practice harder, :)
 2 years ago

AnimalAin Group TitleBest ResponseYou've already chosen the best response.1
I'm sure you'll get it.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.1
i hope i get it the soonest possible, my exam is tomorrow. O.O
 2 years ago
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