Differential Equation Power Series Method

In summary, the Differential Equation Power Series Method is a technique used to solve differential equations by representing the solution as an infinite polynomial. It is used when coefficients are difficult to integrate or when an exact solution is not possible. The method involves substituting the series into the equation and solving for coefficients. It has the advantage of being able to solve a wide range of equations and can provide accurate solutions. However, limitations include the possibility of not finding a series solution, time-consuming coefficient determination, and convergence issues.
  • #1
lclauber
2
0
Differential Equation Power Series Method (Almost done!)

Homework Statement


solve (2x-1)y'+2y=0 using power series.
I'm really close to the correct answer, which is c/(1-2x). I keep getting 2c/(1-2x).
I got the correct radius of convergence, however (1/2)

Homework Equations


shown in my attempt at a solution.

The Attempt at a Solution


attached as a png.
 

Attachments

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  • #2
welcome to pf!

hi lclauberc welcome to pf! :smile:
lclauber said:
I'm really close to the correct answer, which is c/(1-2x). I keep getting 2c/(1-2x).

erm :redface: …

c is arbitrary! :wink:​
 
  • #3
*facepalm* lol.
Thank you!
 

FAQ: Differential Equation Power Series Method

What is the Differential Equation Power Series Method?

The Differential Equation Power Series Method is a technique used to solve differential equations by representing the solution as a power series, which is an infinite polynomial. This method is particularly useful for solving linear differential equations with variable coefficients.

When is the Differential Equation Power Series Method used?

The Differential Equation Power Series Method is used when the coefficients of a differential equation are difficult to integrate or when an exact solution cannot be found using other methods. It is also used when the solution to a differential equation is needed as a series expansion around a particular point.

How does the Differential Equation Power Series Method work?

The Differential Equation Power Series Method involves substituting a power series solution into the differential equation and equating coefficients of like powers. This results in a system of equations that can be solved to determine the coefficients of the power series. The solution can then be expressed as an infinite series.

What are the advantages of using the Differential Equation Power Series Method?

The main advantage of using the Differential Equation Power Series Method is that it can be used to solve a wide range of differential equations, including those with variable coefficients and nonlinear terms. It also provides an accurate solution to the differential equation, as the series can be truncated to any desired degree of accuracy.

Are there any limitations to the Differential Equation Power Series Method?

One limitation of the Differential Equation Power Series Method is that it may not always be possible to find a power series solution to a given differential equation. In addition, it can be time-consuming and tedious to determine the coefficients of the power series, especially for more complex equations. Lastly, the series may not converge for certain values of the independent variable, resulting in an invalid solution.

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