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Proof equality of an equation with exponentials.

  1. May 27, 2013 #1
    Proof if A,B and C are non zero constant:
    [tex]Ae^{jax}+Be^{jbx}=Ce^{jcx}\;\Rightarrow\; a=b=c[/tex]
    The answer from the book involve differentiating it twice and manipulate a, b and c to proof.

    My question is if I differentiate it once:
    [tex]\Rightarrow\;jaAe^{jax}+jbBe^{jbx}=jcCe^{jcx}[/tex]
    So if
    [tex]Ae^{jax}+Be^{jbx}=Ce^{jcx}\;\hbox { and }\;jaAe^{jax}+jbBe^{jbx}=jcCe^{jcx}[/tex]
    Does that already proof a=b=c?
     
  2. jcsd
  3. May 27, 2013 #2

    Dick

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    It's not a proof until you say why you think that proves a=b=c.
     
  4. May 27, 2013 #3
    Can I say if
    [tex]Ae^{jax}+Be^{jbx}=Ce^{jcx}\;\hbox { and }\;jd(Ae^{jax}+jbBe^{jbx})=jcCe^{jcx}\Rightarrow;d=c[/tex]
    and if
    [tex]\;jaAe^{jax}+jbBe^{jbx}=jd(Ae^{jax}+jbBe^{jbx})\Rightarrow\; a=b=d[/tex]

    Therefore a=b=c

    Thanks
    Alan
     
  5. May 27, 2013 #4

    Dick

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    I really don't know where those implications are coming from and I don't see how you got a 'd' out of an expression containing a, b and c.
     
  6. May 27, 2013 #5
    You have written some conditional statements in the form of [itex]P \Rightarrow Q[/itex], but you haven't included any proof of whether they're true or not.

    By direct proof, for instance, you have to show that P being true forces Q to be true.
     
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