Perform the following tasks for the equations below: (1) Find a general solution of the associated homogeneous equation. (2) Use the method of undetermined coefficients to find a particular solution of the given equation. (3) Write down the general solution of the given equation. (4) Find the solution satisfying the given initial conditions. y''-6y'-7y=-9e^{-2t}, \quad y(0)=6, \quad y'(0)=3y ′′ −6y ′ −7y=−9e −2t ,y(0)=6,y ′ (0)=3