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Math Help - Differential Eqn

  1. #1
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    Differential Eqn

    Suppose f:R->R is differentiable everywhere.

    Prove that if f′(x) = af(x) for all x, then f(x) = Aexp(ax) for some constant
    A.

    I've done a lot of fiddling around with this and seem be getting a circular argument. Any help would be greatly appreciated.

    Thanks.
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  2. #2
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    f '(x)=a*f(x)

    or, d(f(x))/f(x)=a*dx

    or,integration[d(f(x))/f(x)]=integration(a*dx)

    or,ln(f(x))=ax+c

    or,f(x)=e^(ax+c)
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  3. #3
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    it's an analysis question - we haven't formally defined integration yet so it has to be solved another way
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