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    Hello there,

    I require some help with a maths problem.

    I need to find the particular integral for a differential equation:

    \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=e^{4x}-5

    I have worked out the complementary function of the equation, however, I don't know entirely which method to use for the particular integral.

    Should I use the y=ax+b method or the exponential method, or a combination of both to find the answer?

    (Methods taken from here: http://www.thestudentroom.co.uk/show...00&postcount=4)

    Thanks =)
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    The point of finding a complementary function, is that you'll end up on the LHS something you can manipulate with the RHS.

    So in this case I would go for  y = Ae^{4x} + b

     y' = 4Ae^{4x} and  y'' = 16Ae^{4x}

     16Ae^{4x} - 12Ae^{4x} + 8Ae^{4x} + 2b = e^{4x} - 5

     12Ae^{4x} + 2b = e^{4x} - 5

    A = 1/12 and b = -5/2

    I have to say it's been almost 2 years since I've done any FP1 so you never know, I might be wrong.
    • Thread Starter
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    That's great thank you very much. That's a great help =)

    Your other post helped me to understand particular integrals a lot more also =)

    Thanks
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    I'm glad to see they're still being used . I have to say on first looking at finding particular integrals, it can seem abit of a punch in the dark at which function you choose, but there is a logic to it, which you can see by examples.
 
 
 
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