Dont know where I went wrong Find the solution to the bounda

Don\'t know where I went wrong

Find the solution to the boundary value problem: d^2y/dt^2 - 5dy/dt + 6y = 0, y(0) = 9, y(1) = 4 The solution is y =

Solution

The auxiliary equation is m²-5m+6=0

Roots are 2&3

Hence general solution is y(t) = c₁e^2t+c₂e^3t

The boundary conditions imply

c₁+c₂=9  

c₁e²+c₂e³=4    ................_> c₂= (4-c₁e²)/ e³

solving thus   

c₁+ (4-c₁e²)/ e³ = 9  

implies c₁= (9 e³ -4) / (e³ -e²) =13.922

c₂= -4.922

thus solution is y(t) = 13.922 e^2t - 4.922e^3t