1. Solve the following homogeneous differential equations: a. y"+6y'+8y = 0, y(0) = 1, y'(0) = 0 b. y"+6y+13y=0 c. y"+6y+9y=0 d. xy"+xy-4y = 0, y(1) = 0, y'(1)=1 2. Give the form of the particular solution y,(t) to be found by the Method of Undetermined Coefficients for the following differential equation: (Do not solve the differential equation) y"-2y-8y-e-te" + e' cos 2t-t sin 4t 3. Solve the initial value problem y+9y=0, y(0) = 0, y'(0) = 0, y"(0) = 1 4. Use the Method of Variation of Parameters to find the general solution of the inhomogeneous differential equation y"-4y'+4y=te² 5. Use the Method of Undetermined Coefficients to find the general solution of the inhomogeneous differential equation y"+y'-6y=3e+t² + cos 2t