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1. 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?
2. (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?
What's the question?
3. (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?
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.
4. this question here
(Original post by RDKGames)
What's the question?
Attached Images

5. 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.
6. (Original post by Iconic_panda)
this question here
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 root while 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.
7. (Original post by Iconic_panda)
this question here
For the particular integral.

TRY

find

sub in ODE to produce a vanishing LHS : 0=0

oh no!

so we try
8. 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
9. 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 root while 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.
10. (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?
Yep
11. thank you
(Original post by RDKGames)
Yep

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