2nd order linear equation solving for a, with boundary conditions.
Hello I'm having problem solving the following:
Let a be a real constant. Consider the equation
]with boundary conditions y(0)=0 and y(6)=0.
For certain discrete values of a, this equation can have non-zero solutions. Find the three smallest values of a for which this is the case.
Enter your answers in increasing order, I need to find a_1, a_2, a_3
I've tried solving using the following Y(x) = C_1 e^((-3+3sqrt(1-4a))x)+C_2 e^((-3+3sqrt(1-4a))x), but i am not getting the right answer.