I am stuck on this homework problem: Exercise2.5.4: Solve the initial value problem y" + 9y = cos(3x) + sin(3x) for y(0) = 2, y0(0) = 1. I tried undetermined coefficient method with yp=Acos(3x) +Bsin(3x) but this seems to cancel out when plugged into the differential equation which does not help. I tried variation of parameter but don't know what I'm doing. Please help!

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.