What is the Solution for Undetermined Coefficients of y''+y'+y=(1-e^-t)?

  • Thread starter kraigandrews
  • Start date
In summary, the undetermined coefficient method is a technique for solving non-homogeneous linear differential equations by assuming the form of the solution and solving for the coefficients. It is typically used for non-homogeneous equations with specific forms, such as polynomials or trigonometric functions. The method involves substituting the assumed solution and its derivatives into the original equation and comparing coefficients. However, it has limitations and cannot be used for non-linear equations or more complex non-homogeneous terms. To use the method effectively, it is important to identify the form of the non-homogeneous term, avoid overlapping with the homogeneous solution, and use a table or chart to organize the coefficients.
  • #1
kraigandrews
108
0

Homework Statement



I am stuck on this and just need to know the form of the solution for undetermined coeffecients of y''+y'+y=(1-e^-t)

my guess is A-Ae^-t but I am not sure
 
Physics news on Phys.org
  • #2
kraigandrews said:

Homework Statement



I am stuck on this and just need to know the form of the solution for undetermined coeffecients of y''+y'+y=(1-e^-t)

my guess is A-Ae^-t but I am not sure
Well, what happened when you tried to work with your guess?
 
  • #3
it didnt work but i was just wondering if the 1 matters.
 

1. What is the undetermined coefficient method?

The undetermined coefficient method is a technique used to solve non-homogeneous linear differential equations. It involves finding a particular solution by assuming the form of the solution and then solving for the coefficients.

2. When is the undetermined coefficient method used?

The undetermined coefficient method is typically used when the differential equation is non-homogeneous and the non-homogeneous term has a specific form, such as a polynomial or trigonometric function.

3. How does the undetermined coefficient method work?

The undetermined coefficient method involves assuming a particular solution in the form of the non-homogeneous term and its derivatives, and then solving for the coefficients using substitution and comparison of coefficients with the original equation.

4. What are the limitations of the undetermined coefficient method?

The undetermined coefficient method is limited to solving linear differential equations with non-homogeneous terms that have a specific form. It cannot be used for non-linear differential equations or non-homogeneous terms with more complex forms.

5. What are some tips for using the undetermined coefficient method effectively?

Some tips for using the undetermined coefficient method effectively include: identifying the form of the non-homogeneous term, making sure the particular solution does not overlap with the homogeneous solution, and using a table or chart to organize the coefficients and their corresponding terms.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
500
  • Calculus and Beyond Homework Help
Replies
1
Views
705
  • Calculus and Beyond Homework Help
Replies
2
Views
189
  • Calculus and Beyond Homework Help
Replies
7
Views
687
  • Calculus and Beyond Homework Help
Replies
7
Views
706
  • Calculus and Beyond Homework Help
Replies
2
Views
322
  • Calculus and Beyond Homework Help
Replies
18
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
330
  • Calculus and Beyond Homework Help
Replies
3
Views
570
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
Back
Top