Question

Particular solution of a nonhomogeneous ODE question

Answer 1

Using method of undetermined coefficients

Answer 2

Would a good guess be for a particular solution be At?

Answer 3

Any ideas @mukushla

Answer 4

\[A_t=at+b\]

Answer 5

So y'=at
y"=a

Answer 6

y'=a ;)

Answer 7

Whoops, and the B will cancel out

Answer 8

so what would be the values of a and b?

Answer 9

Well LHS is -3A+3At+3B

Answer 10

After subbing back into the original equation and multiplying out.

Answer 11

well and?

Answer 12

Wait I had to factor out there didn't I?

Answer 13

I think it's A=1/3 and B=0

Answer 14

u have

-3a+3at+3b=t

it gives 3a=1 and -3a+3b=0 so a=1/3 and b=1/3

Answer 15

Ahh

Answer 16

I don't why I factorised then...

Answer 17

don't why.

Answer 18

and the idea of this problem

when u have a degree \(n\) polynomial on the RHS u need a degree \(n\) polynomial for ur guess.

For this example right hand side is a linear polynomial. For this we will need a linear polynomial guess for the particular solution.

Answer 19

Like Ax+b

Answer 20

So for example if the RHS was x^2-x I would use the form Ax^2+Bx+C

Answer 21

exactly

Answer 22

No wait it would be Ax^3+Bx^2+Cx

Answer 23

why u multiply it by x? it was right

Answer 24

I tried doing it using the Ax^2+Bx+C

Answer 25

Each sides form doesn't match up

Answer 26

When I used the Ax^3+Bx^2+Cx

My y''=6Ax+2B

Answer 27

same question with the RHS x^2-x?

Answer 28

Oops, I should mentioned it was the next question in my text book The question is y''+y'=x^2-x

Answer 29

well here u have a common part between complementary and particular and u must multiply particular by x.

Answer 30

Thanks fo the help, the guessing part is most of the work.

Answer 31

very welcome :)

Answer 32

I'm just try to match up the orders on both sides.

Answer 33

and if don't work out multply across by x.

Answer 34

It's degree?

Answer 35

ahh yes... i think u can do that...match the orders of both side..but i dont know if its work allways or not

Answer 36

All the questions I've done go only as high as degree 3 so i should be ok.