Second order differential equation

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Homework Help Overview

The discussion revolves around solving a second-order differential equation of the form x'' + 3x' + 2x = 1/(1 + e^t). Participants are exploring methods to find the particular solution after identifying the homogeneous solution.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the variation of parameters method as a potential approach for finding the particular solution. There is also mention of the method of undetermined coefficients and its applicability based on the form of the right-hand side of the equation.

Discussion Status

Some participants have shared guidance on methods to approach the problem, with one confirming that the suggested method worked for them. Another participant has introduced a new problem involving a first-order differential equation, indicating ongoing exploration of related topics.

Contextual Notes

There is a transition between different types of differential equations, with participants moving from a second-order to a first-order equation, which may imply varying levels of familiarity with the subject matter.

eidbadr
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hello i need some help here!

solve:

x''+3x'+2x=1/(1+e^t)

well ok the homogeneous solution is c1*e^t+c2*e^2t
but how to determine the particular solution Xp!
 
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Try using the variation of parameters method
 
If the right hand side were a function of the kind one gets as a solution to a "homogenoous linear equation with constant coefficients"- polynomial, exponentian, sine and cosine, or combinations of those- then you could try "undetermined coefficients' but since it is not you will need to try "variation of parameters" as rock.freak667 suggested.
 
thanks that worked,

if you could give me a hint for this one

t*x'=x+sqrt(x^2-t^2)
 

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