How to find Particular integral of this differential eq:

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Homework Help Overview

The discussion revolves around solving a specific differential equation, focusing on finding the particular integral. The subject area includes differential equations and methods for solving them.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to find the complementary function and begins exploring the method for the particular integral but expresses uncertainty about the next steps. Some participants question the correctness of the complementary solution and suggest using variation of parameters, while others seek alternative methods due to concerns about the complexity of this approach.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's approach and suggesting different methods. There is no explicit consensus on the best path forward, but alternative strategies are being considered.

Contextual Notes

Participants are discussing the roots of the characteristic equation and the implications for finding the particular integral, indicating potential misunderstandings or assumptions that may need clarification.

abrowaqas
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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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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.
 
oh yes... thanks LCKurtz..
but Variation of Parameters taking too long..
do you have any other method to solve it..
 
abrowaqas said:
oh yes... thanks LCKurtz..
but Variation of Parameters taking too long..
do you have any other method to solve it..

Maple. :rolleyes:
 

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