How to find Particular integral of this differential eq:

In summary, the conversation is about solving a differential equation with the given function. The participants discuss finding the complementary function and using variation of parameters to find a particular solution. One participant suggests using Maple as an alternative method.
  • #1
abrowaqas
114
0

Homework Statement


Solve the following differential equation

y'''-3y''+2y' = e^x/(1+e^(-x))


Homework Equations





The Attempt at a Solution



first i find the complementary function i-e
Yc= C1 e^x + C2 e^(1+√3)x + C3 (1-√3)x

now i started to find particular integral by

Yp = 1/f(D) e^x/(1+e^(-x))
= e^x 1/f(D+1) 1 /(1+e^(-x))
= e^x 1/f(D+1) e^x/e^x+1

i am stuch here... how i may go now..

can anybody tell me how i find Particular Integral of this question?
 
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  • #2
I think your complementary solution is wrong. The roots of your characteristic equation are 0,1, and 2. Once you fix that you will need to use variation of parameters to get a particular solution of the NH equation.
 
  • #3
oh yes... thanks LCKurtz..
but Variation of Parameters taking too long..
do you have any other method to solve it..
 
  • #4
abrowaqas said:
oh yes... thanks LCKurtz..
but Variation of Parameters taking too long..
do you have any other method to solve it..

Maple. :rolleyes:
 

Related to How to find Particular integral of this differential eq:

1. What is a particular integral?

A particular integral is a specific solution to a differential equation that takes into account the initial conditions of the problem. It is used in conjunction with the general solution to find the complete solution to the differential equation.

2. How do I find the particular integral of a differential equation?

To find the particular integral, you will need to use a method such as the method of undetermined coefficients or the method of variation of parameters. These methods involve finding a particular form of the solution and substituting it into the differential equation to solve for the coefficients.

3. Can I use any method to find the particular integral?

No, the method you use to find the particular integral will depend on the form of the differential equation. Some methods may work better for certain types of equations, so it is important to understand the different methods and choose the appropriate one for your particular equation.

4. Do I need to know calculus to find the particular integral?

Yes, knowledge of calculus is necessary to find the particular integral of a differential equation. You will need to be familiar with integration, derivatives, and other calculus concepts to use the methods for finding the particular integral.

5. Can I find the particular integral by hand or do I need to use a computer?

You can find the particular integral by hand, but it can be a complex and time-consuming process. It may be more efficient to use a computer or calculator to solve the differential equation and find the particular integral. However, it is important to understand the steps involved in finding the particular integral by hand in order to fully understand the solution.

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