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Math Help - For what values of r does the function y = e^rx satisfy

  1. #1
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    For what values of r does the function y = e^rx satisfy

    For what values of r does the function y = e^rx satisfy the equation y'' + 4y' - 45y = 0?
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  2. #2
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    Solve r^2+4r-45=0 do you know why?
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  3. #3
    Junior Member bondesan's Avatar
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    Hello,

    Why don't you just try to plug y = e^rx into the given equation and see what happens? You should notice that e^rx is never equal to zero, so this will lead you to a polinomial equation in r. Solve it and find the roots - they are what you're looking for.
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  4. #4
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    Quote Originally Posted by pickslides View Post
    Solve r^2+4r-45=0 do you know why?
    i do not know why. please explain
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  5. #5
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    An eqn in the form y''+ay'+by=0 has a characteristic eqn r^2+ar+b=0 which gives the solution to the original D.E for real values of r in the form y = e^{rx}

    Did you solve for r ? What did you get?
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  6. #6
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    9, -5
    what is D.E. ?
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  7. #7
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    Better double check your workings, r = -9, 5 , D.E = differential equation.
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  8. #8
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    Quote Originally Posted by pickslides View Post
    Better double check your workings, r = -9, 5 , D.E = differential equation.
    heehee my mistake thank you!
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