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Math Help - exponential differentiation

  1. #1
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    exponential differentiation

    Hi, I need to show that y=(Ax+B).e^3x is a solution to y''-6y'+9y=0
    I'm getting

    y'=e^3x(3Ax+3B+A)

    y''=3e^3x(2A+3Ax+3B)

    When I sub these values back into the condition above its not working out.

    Thank you
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  2. #2
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    Quote Originally Posted by slaypullingcat View Post
    Hi, I need to show that y=(Ax+B).e^3x is a solution to y''-6y'+9y=0
    I'm getting

    y'=e^3x(3Ax+3B+A)

    y''=3e^3x(2A+3Ax+3B)

    When I sub these values back into the condition above its not working out.

    Thank you
    Show some details - I got it to work!
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  3. #3
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    Your calculations for y' and y'' are correct. I derived:

    \begin{aligned}<br />
y''-6y'+9y&=(9Ax+9B+6A)e^{3x}\\<br />
&-(18Ax+18B+6A)e^{3x}\\<br />
&+(9Ax+9B)e^{3x}\\<br />
&=0.<br />
\end{aligned}
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  4. #4
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    Your derivatives are correct, and the proposed y is indeed a solution. Check your calculations again (hint: factor out e^{3x}).
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  5. #5
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    Did it it work with the first and second derivative values I gave? Or did I differentiate incorrectly?
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  6. #6
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    Quote Originally Posted by slaypullingcat View Post
    Did it it work with the first and second derivative values I gave? Or did I differentiate incorrectly?
    Like the others have said - the derivatives are correct. If you show some work, maybe we can show you were you messed up
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