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

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lilMissMindsetBest ResponseYou've already chosen the best response.1
@AnimalAin this.
 one year ago

partyrainbow276Best ResponseYou've already chosen the best response.0
Awesome! u did it write
 one year ago

lilMissMindsetBest ResponseYou've already chosen the best response.1
this is my answer: 2Ae^x + B + Cx = 5e^x 162x
 one year ago

partyrainbow276Best ResponseYou've already chosen the best response.0
lets see...... AWESOME AWESOME :) thats right good job
 one year ago

AnimalAinBest 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.
 one year ago

partyrainbow276Best ResponseYou've already chosen the best response.0
lilmissmindset is right thats what i got for my answer
 one year ago

AnimalAinBest ResponseYou've already chosen the best response.1
That's the problem we did before.....
 one year ago

lilMissMindsetBest 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 \[=C _{1} \cos 3x+ C _{2} \sin3x + \frac{ 1 }{ 2 } e ^{x} 18xy \]
 one year ago

lilMissMindsetBest ResponseYou've already chosen the best response.1
there's no y after 18x SORRY
 one year ago

AnimalAinBest ResponseYou've already chosen the best response.1
Lets look at this in more detail.
 one year ago

lilMissMindsetBest ResponseYou've already chosen the best response.1
and our answer is 5/2 e^x 162x
 one year ago

lilMissMindsetBest ResponseYou've already chosen the best response.1
i thought, maybe there's something wrong with me, getting the solution after all
 one year ago

AnimalAinBest 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?
 one year ago

lilMissMindsetBest ResponseYou've already chosen the best response.1
ok with that part,
 one year ago

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

AnimalAinBest 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.
 one year ago

lilMissMindsetBest ResponseYou've already chosen the best response.1
owwww. i understand,
 one year ago

AnimalAinBest 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\[ 9y_{p2} = 162x \implies y_{p2} =19x\]
 one year ago

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

lilMissMindsetBest 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,
 one year ago

AnimalAinBest 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.
 one year ago

AnimalAinBest ResponseYou've already chosen the best response.1
I hope you've got this; you're wearing me out....LOL
 one year ago

lilMissMindsetBest 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,
 one year ago

lilMissMindsetBest ResponseYou've already chosen the best response.1
i get it, i'm just confused on some parts.
 one year ago

AnimalAinBest 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.
 one year ago

lilMissMindsetBest ResponseYou've already chosen the best response.1
i'll practice harder, :)
 one year ago

AnimalAinBest ResponseYou've already chosen the best response.1
I'm sure you'll get it.
 one year ago

lilMissMindsetBest ResponseYou've already chosen the best response.1
i hope i get it the soonest possible, my exam is tomorrow. O.O
 one year ago
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