# Undetermined Coefficients, just a piece i with

• rygza
In summary, the process of finding the coefficients of Yp involves setting the coefficients of similar terms on both sides of the equation equal to each other. This includes the coefficients of the e^x terms, the sinx terms, and the xsinx terms. Joining the sinx term and xsinx term together is the correct method, while the method of adding the two terms together is not correct.
rygza
Undetermined Coefficients, just a piece i need help with please

In one of the last steps in trying to find the Coefficients of Yp (particular solution), I am supposed to set coefficients of similar terms equal to each other. Here's where i need help:
i have
A(e^x) + (-2B-2C+2F+E)sinx + (2B+F-2C-2E)cosx + (B+2C) xsinx + (C-2B)xcosx = (e^x)+xcosx

I set: A=1, -2B-2C+2F+E = 0, 2B+F-2C-2E=0, B+2C=0, and C-2B=1

is this the correct method?

OR

am i supposed to join the sinx term and xsinx terms (second and fourth terms from my first equation) together like this:

(-2B-2C+2F+E+Bx+2Cx)sinx
?

rygza said:
In one of the last steps in trying to find the Coefficients of Yp (particular solution), I am supposed to set coefficients of similar terms equal to each other. Here's where i need help:
i have
A(e^x) + (-2B-2C+2F+E)sinx + (2B+F-2C-2E)cosx + (B+2C) xsinx + (C-2B)xcosx = (e^x)+xcosx

I set: A=1, -2B-2C+2F+E = 0, 2B+F-2C-2E=0, B+2C=0, and C-2B=1

is this the correct method?
Yes, this is correct. The equation above has to be identically true for all x. The only way this can happen is for the coefficients of the e^x terms on each side to be equal, the coefficients of the sinx terms have to be equal, and so on.

The method below is not correct.
rygza said:
OR

am i supposed to join the sinx term and xsinx terms (second and fourth terms from my first equation) together like this:

(-2B-2C+2F+E+Bx+2Cx)sinx
?

Mark44 said:
Yes, this is correct. The equation above has to be identically true for all x. The only way this can happen is for the coefficients of the e^x terms on each side to be equal, the coefficients of the sinx terms have to be equal, and so on.

The method below is not correct.

thanks!

## 1. What is the Undetermined Coefficients method?

The Undetermined Coefficients method is a technique used in solving differential equations with constant coefficients. It involves finding a particular solution to the equation by assuming a form for the solution and determining the unknown coefficients.

## 2. How does the Undetermined Coefficients method work?

The Undetermined Coefficients method works by assuming a form for the particular solution to the differential equation, typically based on the form of the non-homogeneous function. This form includes unknown coefficients which are then determined by substituting the assumed solution into the original equation and solving for the coefficients.

## 3. When is the Undetermined Coefficients method used?

The Undetermined Coefficients method is used when solving non-homogeneous linear differential equations with constant coefficients. It is particularly useful when the non-homogeneous function has a simple form, such as a polynomial, exponential, or trigonometric function.

## 4. What are the limitations of the Undetermined Coefficients method?

The Undetermined Coefficients method is only applicable to linear differential equations with constant coefficients. It also requires the non-homogeneous function to have a simple form, which may not always be the case. In some cases, the method may fail and a different approach, such as variation of parameters, may be necessary.

## 5. Can the Undetermined Coefficients method be used to solve non-linear differential equations?

No, the Undetermined Coefficients method is only applicable to linear differential equations. For non-linear equations, other methods such as separation of variables, substitution, or numerical methods may be used.

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