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FP2: 2nd order differential equations - Substitution watch

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    I've found the complementary integral and got y=e^-x(Acosx + Bsinx) but I wasn't sure what to use to find my particular integral! Would it be y=lamdaE^mx or y=lamdaE^-x
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    (Original post by creativebuzz)
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    I've found the complementary integral and got y=e^-x(Acosx + Bsinx) but I wasn't sure what to use to find my particular integral! Would it be y=lamdaE^mx or y=lamdaE^-x
    You can't use y= \lambda e^{-x} because it's part of the C.I, so what would you use instead?
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    (Original post by Jordan\)
    You can't use y= \lambda e^{-x} because it's part of the C.I, so what would you use instead?
    λe^-x is not part of the C.F?
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    (Original post by Gome44)
    λe^-x is not part of the C.I?
    Oh I read it wrong, I just saw it in the C.F :getmecoat: It would be fine to just use λe^-x then wouldn't it?
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    (Original post by Gome44)
    λe^-x is not part of the C.F?
    Yup, I've got the answer now thanks!

    Would you mind giving me a hand on this question
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    I've got as far as dz/dx = cosx

    dy/dx = cosxdy/dx

    and I tried to use the product rule to find d^y/dx^2 and I got -sinxdy/dx + cosxd^2y/dx^2 or did I go wrong somewhere?
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    (Original post by creativebuzz)
    Yup, I've got the answer now thanks!

    Would you mind giving me a hand on this question
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    I've got as far as dz/dx = cosx

    dy/dx = cosxdy/dx

    and I tried to use the product rule to find d^y/dx^2 and I got -sinxdy/dx + cosxd^2y/dx^2 or did I go wrong somewhere?
    This part in bold is incorrect.  \dfrac{dy}{dx} = \dfrac{dz}{dx} \dfrac{dy}{dz} , so what you should end up with is  \dfrac{dy}{dx} = \cos (x) \dfrac{dy}{dz}

    You then need to use implicit differentiation
 
 
 
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