1. ## 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

2. Originally Posted by slaypullingcat
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!

3. Your calculations for $y'$ and $y''$ are correct. I derived:

\begin{aligned}
y''-6y'+9y&=(9Ax+9B+6A)e^{3x}\\
&-(18Ax+18B+6A)e^{3x}\\
&+(9Ax+9B)e^{3x}\\
&=0.
\end{aligned}

4. Your derivatives are correct, and the proposed y is indeed a solution. Check your calculations again (hint: factor out $e^{3x}$).

5. Did it it work with the first and second derivative values I gave? Or did I differentiate incorrectly?

6. Originally Posted by slaypullingcat
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