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, 03:58 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, 04:20 PMJester
- May 12th 2009, 04:26 PMScott H
Your calculations for and are correct. I derived:

- May 12th 2009, 04:27 PMSpec
Your derivatives are correct, and the proposed y is indeed a solution. Check your calculations again (hint: factor out ).

- May 12th 2009, 04:28 PMslaypullingcat
Did it it work with the first and second derivative values I gave? Or did I differentiate incorrectly?

- May 12th 2009, 04:30 PMJester