solve the boundary value problem y\'\'+25y = 0 with y(0)=0 and y(pi)=0 Solution Characteristic equation: r^2 - 11r + 28 = (r - 7)(r - 4) = 0 ==> r = 7, 4. So, y = Ae^(7t) + Be^(4t). Use the boundary values to find A and B. y(0) = 1 ==> 1 = A + B y(1) = 7 ==> 7 = Ae^7 + Be^4. Solving for A and B: A = (7 - e^4)/(e^7 - e^4) and B = (e^7 - 7)/(e^7 - e^4)..