Help solving a second order ODE with repeated roots,

[adam640]

Help solving a second order ODE with repeated roots, urgent!

I have a differential equaition

d2y/dx2 - 6dy/dx + 9y = 0

I have found the general solution to be

y = (Ax + B)e^3x

Now I need to find the solutions to A and B so that...

when y = 4, x = 0
when y = 49.e¹⁵, x = 5

I literally have no idea where to start with this question and I have this and a few others of a similar format due in a couple of hours, so any help is greatly appreciated. I understand the other methods for ODE's but I do not have any notes for this method and have been unable to find any resources online.

Any help is greatly appreciated!

Thanks,

Adam

 

[ehild]

Plug in y=4, x=0. You get an equation for the unknowns A and B. Then plug in y=49 e¹⁵, x=5 (simplify, do not evaluate!) It is an other equation for A, B. Two equations for two unknowns. Solve.

ehild

 

[adam640]

Thanks... I didn't think it would be that simple! I was going far too deep into this question.

It's been a long night! haha

 

[ehild]

Maths is simpler than you imagine

ehild