These are two separate problems. Please work out these problems the way they are listed and then box your answer. I don't think any of the red boxes are supposed to have any listed answers.

For the differential equation y' + 161/ + 643} : 1:3 Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is _ List the complementary EJnctions (the functions that make up the complementary solution) _ . 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) - Therefore the particular solution must be made up of the Functions Substituting these into the differential equation, we nd the particular solution is Part 3: Solve the non-homogeneous equation 1f + 163/ + 643; : :73 has general solution (remember to use the format I gave you in your correct answer to the complementary snctions above) - Now that we have the general solution solve the [VP gm) 2 3 11(0) : 5 For the differential equation 3;" + 103/ + 25y : sin(32) Part 1: Solve the homogeneous equation The differential operator for the homogeneous equation is List the complementary fiJnctions 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 differential operator From above) Therefore the particular solution must be made up of the Functions Substituting these into the differential equation, we nd the particular solution is Part 3: Solve the non-homogeneous equation y" + 10y'+ 253; = 5in(3:1:) has general solution (remember to use the format [ gave you in your correct answer to the complementary functions above) _ Now that we have the general solution solve the IVP 19(0) = *7 11(0) 2 3