1. ## Boundary Value Problem

Find the values of $\lambda$ for which the given boundary problem has a unique solution and find the solution

$y''+4y'+(4+9\lambda)y=0$
y(0)=1, y(2)=0

Please help. I have tried using a new dependent variable u where y=s(x)u but I am not sure if this is right

2. I would say the first step should be to find the general solution (without the constants of integration determined). You've got a homogeneous equation, so no particular solution is required. What did you get for that?

3. I got $y(x)=Ae^{-2x}cos3x+Be^{-2x}sin3x$ but i don't think that's even right

4. I'm afraid it can't possibly be correct: there are no $\lambda$'s in your solution. It's a second-order linear ODE with constant coefficients. I would just use the guess-and-check method (or undetermined coefficients).

5. Okay, thanks. I will try after I get some sleep (it's 3.30 am here :P ). Thanks again.

6. Did you manage to get a solution?

7. Yes I did. Thanks for asking!