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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- May 12th 2009, 02:58 PMslaypullingcatexponential 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 - May 12th 2009, 03:20 PMJester
- May 12th 2009, 03:26 PMScott H
Your calculations for $\displaystyle y'$ and $\displaystyle y''$ are correct. I derived:

$\displaystyle \begin{aligned}

y''-6y'+9y&=(9Ax+9B+6A)e^{3x}\\

&-(18Ax+18B+6A)e^{3x}\\

&+(9Ax+9B)e^{3x}\\

&=0.

\end{aligned}$ - May 12th 2009, 03:27 PMSpec
Your derivatives are correct, and the proposed y is indeed a solution. Check your calculations again (hint: factor out $\displaystyle e^{3x}$).

- May 12th 2009, 03:28 PMslaypullingcat
Did it it work with the first and second derivative values I gave? Or did I differentiate incorrectly?

- May 12th 2009, 03:30 PMJester