Help solving a second order ODE with repeated roots,

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Homework Help Overview

The discussion revolves around solving a second order ordinary differential equation (ODE) with repeated roots, specifically the equation d²y/dx² - 6dy/dx + 9y = 0. The original poster has identified the general solution but is seeking assistance in determining specific constants based on given conditions.

Discussion Character

  • Exploratory, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to find constants A and B in the general solution by applying specific values for y and x. Some participants suggest substituting these values into the general solution to create a system of equations.

Discussion Status

Participants have provided guidance on how to set up equations based on the conditions given by the original poster. There is an acknowledgment of the simplicity of the approach, indicating a productive direction in the discussion.

Contextual Notes

The original poster expresses urgency due to a deadline and mentions a lack of notes on this particular method, which may influence their understanding and approach to the problem.

adam640
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Help solving a second order ODE with repeated roots, urgent!

I have a differential equaition

d2y/dx2 - 6dy/dx + 9y = 0

I have found the general solution to be

y = (Ax + B)e3x

Now I need to find the solutions to A and B so that...

when y = 4, x = 0
when y = 49.e15, x = 5

I literally have no idea where to start with this question and I have this and a few others of a similar format due in a couple of hours, so any help is greatly appreciated. I understand the other methods for ODE's but I do not have any notes for this method and have been unable to find any resources online.

Any help is greatly appreciated!

Thanks,

Adam
 
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Plug in y=4, x=0. You get an equation for the unknowns A and B. Then plug in y=49 e15, x=5 (simplify, do not evaluate!) It is an other equation for A, B. Two equations for two unknowns. Solve.

ehild
 


Thanks... I didn't think it would be that simple! I was going far too deep into this question.

It's been a long night! haha
 


Maths is simpler than you imagine:smile:

ehild
 

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