# Very simple diff eq [concept help needed for exam] (1 Viewer)

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#### Tom McCurdy

1. The problem statement, all variables and given/known data

Find the exact solution to this problem
y'=4x–y+9;y(0)=6

3. The attempt at a solution

I am panicing because I have an exam tomorrow and I can't remeber a lot of the basics for diff eq. I tried to solve this using 2nd order style...

first I made it

y'-y=4x+9

For natural solution i do
r+1=0
r=-1

natural solution = A*e^(-x)

How do I get the forced soution?

And how would I do it on a second order equation so like

y''+By'+y = some x terms

I know how to do natural solutions... its the forced that keeps getting me

#### d_leet

You do realize that that is a first order differential equation right? Do you know the standard method of integrating factors for finding the solution of a first order differential equation?

#### Tom McCurdy

I am trying to avoid first order methods, I would like to be able to solve it using second order method... since r is a real root it would take the natural form A*e(-rx)

Really I guess I picked a bad example... I thought it would be easier than second order... I am trying to figure out how to solve for a second order "forced solution"

#### d_leet

Why are you trying to avoid first order methods for a first order equation? It really is easiest to just find an integrating factor and solve the equation that way.

#### Tom McCurdy

I know its the easiest way, but I don't have any first order problems on my upcomming exam, I just thought it would be easier to learn how to do forced solutions on a first order problem (which I don't even know if it is possilbe) I know how to do the integrating factor method.

S

#### SGT

##### Guest
If your forcing function is a polynomial, the particular solution will be a polynomial of the same degree. In your case
$$y_p = Ax + B$$
Substitute $$y_p$$ and its derivative in the differential equation to obtain the parameters A and B.

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