Second order differential equations

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Homework Help Overview

The discussion revolves around finding the general solution to a second order differential equation, specifically addressing the treatment of the expression 20 - e^x in relation to polynomial functions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore whether the expression 20 - e^x can be considered a polynomial and discuss its nature as a sum of functions. Questions arise regarding the correct form for a particular solution in the context of the differential equation.

Discussion Status

Some participants have provided guidance on the form of the particular solution, suggesting A + Be^{2x}, while others question the original poster's terminology regarding polynomials. The discussion reflects varying interpretations and attempts to clarify the problem.

Contextual Notes

There is mention of the associated homogeneous equation and the need for a general solution, indicating a structured approach to the problem. However, the original poster expresses uncertainty about their progress.

fan_boy17
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Homework Statement



finding the general solution. I would like to know if the 20-e^x will be treated as a sum of a polynomial?

Homework Equations





The Attempt at a Solution

 

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fan_boy17 said:

Homework Statement



finding the general solution. I would like to know if the 20-e^x will be treated as a sum of a polynomial?

Homework Equations





The Attempt at a Solution


20 - ex is not a polynomial. A search on wikipedia will turn up the definition of a polynomial.
 
It is, of course, the sum of two functions. Did you really mean to say "polynomial"?

You should look for a "particular solution" of the form A+ Bex.
 
HallsofIvy said:
It is, of course, the sum of two functions. Did you really mean to say "polynomial"?

You should look for a "particular solution" of the form A+ Bex.

That's a typo, Halls meant ##A+Be^{2x}##.
 
can anyone help with solving it :(
 
fan_boy17 said:
can anyone help with solving it :(

What are you stuck on? Have you solved the associated homogeneous equation for its general solution ##y_c##? Have you tried looking for a particular solution of the NH equation of the form ##y_p=A + Be^{2x}## as has been suggested? It is all straightforward. Show us what you have so far.
 

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