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

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:
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) (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

==> , .

As such, the general solution ought to be for any arbitrary constants A and B, and NOT as you mentioned.
I have done the necessary correction to your problem. I guess you will be able to do it now.
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