SOLUTION: consider the differential equation 2y'' -13y' -7y = 0 a. Show that, for any constants A and B, the following is a solution to the above differential equation: {{{ y = Ae^(-9x)+B

Algebra ->  Test -> SOLUTION: consider the differential equation 2y'' -13y' -7y = 0 a. Show that, for any constants A and B, the following is a solution to the above differential equation: {{{ y = Ae^(-9x)+B      Log On


   

Question 1183480: consider the differential equation 2y'' -13y' -7y = 0
a. Show that, for any constants A and B, the following is a solution to the above differential equation: +y+=+Ae%5E%28-9x%29%2BBe%5E%28x%2F3%29+
b. Find the values A and B that make the above general solution into a solution for the following initial value problem: 2y'' - 13y' - 7y = 0 ; y(0) = 3, y'(0) = -5
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Your differential equation is 2y'' -13y' -7y = 0, which is a homogeneous linear 2nd order ODE with constant coefficients. As such, its characteristic equation is

2%2Alambda%5E2+-+13%2Alambda+-+7+=+%282%2Alambda+%2B+1%29%28lambda+-+7%29+=+0
==> lambda+=+-1%2F2, lambda+=+7.

As such, the general solution ought to be y+=+A%2Ae%5E%28-x%2F2%29+%2B+B%2Ae%5E%287x%29 for any arbitrary constants A and B, and NOT +y+=+Ae%5E%28-9x%29%2BBe%5E%28x%2F3%29+ as you mentioned.
I have done the necessary correction to your problem. I guess you will be able to do it now.