Describing the form of a second-order D.E.

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SUMMARY

The discussion centers on solving the second-order differential equation d²y/dx² + 4(dy/dx) + 20y = 10e⁻²ˣcos(rx). Participants emphasize the importance of first determining the general solution of the homogeneous equation d²y/dx² + 4(dy/dx) + 20y = 0, followed by finding a particular solution that combines e⁻²ˣcos(rx) and sin(rx). The solutions are characterized by their exponential decay as x increases, attributed to the negative exponent in the term e⁻²ˣ.

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joriarty
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Hi;
I'm having a little trouble with a maths assignment, could someone please give me a few pointers? Bear in mind this is an assignment, worth marks towards my course, so please don't give me any answers! I'm just not exactly sure how I should approach this question. A brief explanation of the theory that would help me solve it should help a lot.

Thanks! :smile:

Write up to three sentences on what the form of a particular solution of the following equation should be. Explain why any solution decreases exponentially in magnitude as x increases.

d2y/dx2 + 4(dy/dx) + 20y = 10e-2xcos(rx)
 
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Welcome to PF!

Hi joriarty! Welcome to PF! :wink:

First find a "general solution", ie to the equation d2y/dx2 + 4(dy/dx) + 20y = 0

and then find a "particular solution" to the whole equation (which, I'm guessing, will be a combination of e-2x cos(rx) and sin(rx) ) :smile:
 

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