Solve the following linear differential equations with constant coefficients, by the method of undetermined coefficients: 1. "+ 4y + 13y = e-2r Hint: y, = Ae-2r, A = 1/9 2. /" - 5y + by = 2e Hint: yy = Ae", A = 1 3. y/" - 2y - 3y = 3e Hint: y, = Ae2*, A = -1 4. /"+ 2y + y = 3e- Hint: y, = Ar'e-, A= !! 5. /'+ 2y + 17y = e" +2 Hint: y, = Ae-2=, A = , B = %3D 6. /' - 2y - 8y = de - 21e-3 Hint: y = Ae2 + Be-3r, A = -, B = -3 7. y" - 2y +y = Hint: y, = Ar'e", A = } 8. " -/ = 5e" - sin 2 Hint: yp = Are" + B sin 2r +C cos 2r, A = 5, B =, C = - 9. " + 8y = 4 sin z + cos e