Differential Equation Method OF UNDETERMINED COEFF

In summary, the conversation discusses the difficulty of solving a differential equation using the Method of Undetermined Coefficients. The individual has tried guessing solutions such as (At + B)e^(-t) and Ae^(-t), but they do not work. There is also a mention of a possible error in the book's answer.
  • #1
FahimP
14
0

Homework Statement


I hav been trying to solve this differential equation by Method of Undetermined Coefficients for a long time.

y"-2y'-3y=-3te^(-t) ......

We are supposed to guess a solution then differentiate and go from there. I guessed
y = (At + B)e^(-t) .... but this does not work. ... can someone help me on this ... I have also tried y = Ae^(-t) but this also doesn't work. Is it possible the book answer is wrong ?


Homework Equations





The Attempt at a Solution

 
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  • #2
You first need to solve the homogeneous equation. What solution do you get to that?
 
  • #3
FahimP said:

Homework Statement


I hav been trying to solve this differential equation by Method of Undetermined Coefficients for a long time.

y"-2y'-3y=-3te^(-t) ......

We are supposed to guess a solution then differentiate and go from there. I guessed
y = (At + B)e^(-t) .... but this does not work. ... can someone help me on this ... I have also tried y = Ae^(-t) but this also doesn't work. Is it possible the book answer is wrong ?

Of course it's possible the book is wrong. It is also possible that you are wrong. You shouldn't have to "guess" what to try if you have the complementary solution.

I suggest you re-check your work for Ae-t. And if you get an answer you can always check it for yourself by plugging it into the DE.
 

FAQ: Differential Equation Method OF UNDETERMINED COEFF

What is the Differential Equation Method of Undetermined Coefficients?

The Differential Equation Method of Undetermined Coefficients is a technique used to solve certain types of nonhomogeneous linear differential equations. It involves finding a particular solution based on the form of the nonhomogeneous term in the equation.

What types of nonhomogeneous terms can be solved using this method?

This method is most commonly used for nonhomogeneous terms that are polynomials, exponential functions, sine/cosine functions, and combinations of these. It can also be used for some other special types of nonhomogeneous terms.

3. How does the Differential Equation Method of Undetermined Coefficients work?

The method involves finding a particular solution by assuming a form for the solution based on the nonhomogeneous term, and then solving for the undetermined coefficients in that assumed solution. These coefficients are then substituted back into the assumed solution to obtain the particular solution.

4. When is it appropriate to use this method?

This method is most appropriate for solving nonhomogeneous linear differential equations with constant coefficients. It is also useful when the nonhomogeneous term is a function that can be easily integrated or differentiated.

5. Are there any drawbacks to using the Differential Equation Method of Undetermined Coefficients?

While this method can be very effective for certain types of nonhomogeneous terms, it may not work for more complicated or unusual nonhomogeneous terms. In these cases, other methods such as variation of parameters or the Laplace transform may be more suitable.

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