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Math Help - Differentiating y= Acosαx + Bsinαx and finding Constants

  1. #1
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    Differentiating y= Acosαx + Bsinαx and finding Constants

    Don't really know what to do with this one, any help welcome

    If A, B and α are constants, independent of x, and

    y= Acos
    αx + Bsinαx

    Evaluate the derivates
    y'=dy/dx
    y^n=d^2y/dx^2


    Determine values of A, B and α such that y satisfies
    y^n+y=0 and y(0)=0, y'(0)=1

    I've tried to differentiate y
    y'=
    -αAsinαx + αBcosαx
    y'=αBcosαx - αAsinαx

    y^n=
    αBsinαx + ααAcosαx
    y^n=ααAcosαx - ααBsinαx
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  2. #2
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    Quote Originally Posted by zombieguy View Post
    Don't really know what to do with this one, any help welcome

    If A, B and α are constants, independent of x, and

    y= Acosαx + Bsinαx

    Evaluate the derivates
    y'=dy/dx
    y^n=d^2y/dx^2

    Determine values of A, B and α such that y satisfies
    y^n+y=0 and y(0)=0, y'(0)=1

    I've tried to differentiate y
    y'=-αAsinαx + αBcosαx
    y'=αBcosαx - αAsinαx

    y^n=αBsinαx + ααAcosαx
    y^n=ααAcosαx - ααBsinαx
    The expression y^n=\frac{d^2y}{dx^2} doesn't really make any sense to me. Is y^n supposed to be the nth derivative? Equal to the 2nd derivative?
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  3. #3
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    y^n is equal to the 2nd derivate
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