for this question, why is P.I t cube instead of t square, is there a way of knowing the power of t straight away?
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Iconic_panda
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- 10-03-2018 19:17
Last edited by Iconic_panda; 10-03-2018 at 19:20. -
RDKGames
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- 10-03-2018 19:18
(Original post by Iconic_panda)
for this question, why is P.I t cube instead of t square, is there a way of knowing the power of t straight away? -
tiny hobbit
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- 10-03-2018 19:22
(Original post by Iconic_panda)
for this question, why is P.I t cube instead of t square, is there a way of knowing the power of t straight away?
Similarly, if you already had a e^t term in the CF (just that, not multiplied by some more algebra), then you'd have your PI as te^t. -
Iconic_panda
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- 10-03-2018 19:22
this question here
(Original post by RDKGames)
What's the question? -
Iconic_panda
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- 10-03-2018 19:23
my CF only have t in there, no t square, can you please check the question below?
(Original post by tiny hobbit)
I'll guess that you already have a t squared term in your CF. You therefore have to multiply by another t.
Similarly, if you already had a e^t term in the CF (just that, not multiplied by some more algebra), then you'd have your PI as te^t. -
RDKGames
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- 10-03-2018 19:28
(Original post by Iconic_panda)
this question here
The general rule of thumb, is that if your auxiliary eq. has a repeated rootwhile your RHS of the ODE has
, then the suggested P.I. is
. Here, we have the RHS as
therefore we go up one in the power of
on our P.I. as well, hence we use
Have a good look here starting 'In a nutshell...' (particularly the P.I. choice section) to get a solid understanding of how to deal with all types of ODE's at A-Level.Last edited by RDKGames; 10-03-2018 at 19:57. -
NotNotBatman
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- 10-03-2018 19:35
(Original post by Iconic_panda)
this question here
TRY
find
sub in ODE to produce a vanishing LHS : 0=0
oh no!
so we try
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Iconic_panda
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- 10-03-2018 20:04
ah right!
what if it keeps on not working hahha, do we keep going up the power?(Original post by NotNotBatman)
For the particular integral.
TRY
find
sub in ODE to produce a vanishing LHS : 0=0
oh no!
so we try
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Iconic_panda
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- 10-03-2018 20:57
I got another question, what if the RHS is a combination of two, let say 5 sinx + e^x. would we try PI as a sin x+ b cos x +c e^x, i.e the combination of two as well?
(Original post by RDKGames)
The auxiliary equation has a repeated root, 2, which is also in
The general rule of thumb, is that if your auxiliary eq. has a repeated rootwhile your RHS of the ODE has
, then the suggested P.I. is
. Here, we have the RHS as
therefore we go up one in the power of
on our P.I. as well, hence we use
Have a good look here starting 'In a nutshell...' (particularly the P.I. choice section) to get a solid understanding of how to deal with all types of ODE's at A-Level. -
RDKGames
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- 10-03-2018 20:58
(Original post by Iconic_panda)
I got another question, what if the RHS is a combination of two, let say 5 sinx + e^x. would we try PI as a sin x+ b cos x +c e^x, i.e the combination of two as well? -
Iconic_panda
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- 10-03-2018 21:02
thank you
(Original post by RDKGames)
Yep
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