Thread: 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

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!

Your calculations for and are correct. I derived:

Your derivatives are correct, and the proposed y is indeed a solution. Check your calculations again (hint: factor out ).

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

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