Question

Solve the boundary-value problem.
y'' + 5y' - 6y = 0 , y(0) = 0 , y(2) = 1

Answer 1

y = c1 e^-6x + c2 e^x

Plug in your boundary conditions, and you get

c1 + c2 = 0
c1/e^12 + c2/e^2 = 1

Now just solve for c1 and c2