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Second ODE

Hi , I am trying to understand this and check if I am doing it right if some one can help , it's about finding the exact solution of second ODE , so if
Y ''+4y'-4y = cost t - sint

I could easily solve the homogenous equation and fnd the roots ..etc , but what the right hand side is it right if I do it as y = A cost + B sint then find y ' and y '' and substitute in the above equation

Is that right ??

Thanks
Original post by meme12
Hi , I am trying to understand this and check if I am doing it right if some one can help , it's about finding the exact solution of second ODE , so if
Y ''+4y'-4y = cost t - sint

I could easily solve the homogenous equation and fnd the roots ..etc , but what the right hand side is it right if I do it as y = A cost + B sint then find y ' and y '' and substitute in the above equation

Is that right ??

Thanks


The RHS has an extra t in it. Is that a typo? If it is, your plan is right.
Original post by meme12
Hi , I am trying to understand this and check if I am doing it right if some one can help , it's about finding the exact solution of second ODE , so if
Y ''+4y'-4y = cost t - sint

I could easily solve the homogenous equation and fnd the roots ..etc , but what the right hand side is it right if I do it as y = A cost + B sint then find y ' and y '' and substitute in the above equation

Is that right ??

Thanks


Yes, that's right. However, for future reference, note that you wouldn't be able to do that if the RHS was like the solution of the homogenous equation. In that case, you have to multiply your trial solution by an appropriate power of t.
Reply 3
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Great444
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Original post by tiny hobbit
The RHS has an extra t in it. Is that a typo? If it is, your plan is right.


What do you mean , no
Reply 4
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Great444
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I forget to write that y(0)=1 and y'(0)=1
Original post by meme12
What do you mean , no


It says cost t -....

Was that second t intended? If it is, you'll need more terms in your particular integral.
(edited 9 years ago)
Reply 6
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Great444
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Yes it's sint+cost
Reply 7
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Great444
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What am suppose to do
Reply 8
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Am getting wrong answer for some reason I can find the value of A but B Cancel each other and seem that some thing wrong
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Original post by meme12
Am getting wrong answer for some reason I can find the value of A but B Cancel each other and seem that some thing wrong


Can you post some working so we can see where you're going wrong?
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Original post by davros
Can you post some working so we can see where you're going wrong?

Hi I will attach a copy of what I did I will write the question here please check did I do it right
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image.jpg518.6KB
Reply 12
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The question is y"+4y'+13y = 12 cost -4 sint

y(0) =1 y'(0)=1
Reply 13
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TeeEm
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Original post by meme12
The question is y"+4y'+13y = 12 cost -4 sint

y(0) =1 y'(0)=1


I checked the Particular Integral by D-Operator and I got y = cost, which is what you have
(edited 9 years ago)
Reply 14
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Great444
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Thanks Tee , What does that mean , does that mean my answer is right ?
Reply 15
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I will have cost not - cost when substitute a and b
Reply 16
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Original post by meme12
I will have cost not - cost when substitute a and b


yes sorry I typed -cost but it should be cost
so you are correct
Reply 17
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Great444
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Thanks :smile:
Reply 18
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TeeEm
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no worries

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