For the differential equation y"+6y +9y= r Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is D-+6D+9 List the complementary functions (the functions that make up the complementary solution) -3x-3x A.When you get this answer correct it will give you the format for the complementary solution that you must use below. Part 2: Find the particular solution To solve the non-homogeneous differential equation, we look for functions annihilated by the differential operator (a multiple of the operator given above) D(D+6D+9) Therefore the particular solution must be made up of the functions 1 Substituting these into the differential equation, we find the particular solution is Part 3: Solve the non-homogeneous equation y' + 6y + 9y =r has general solution (remember to use the format I gave you in your correct answer to the complementary functions above) Now that we have the general solution solve the IVP y(0) = -7 y (0) = -3

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