# math285, week of october 13

Homework (due by Tuesday, 10.21):

Solve using variation of parameters:

1. $y”+9y=\sec(3t);$
Answer:$$(1/9)\cos(3t)\ln|\cos(3t)|+(1/3)t\sin(3t)+C_1\cos(3t)+C_2\sin(3t)$$.
2. $y”+2y’+y=e^{-t}/t.$
Answer: $$e^{-t}t\ln{t}+C_1e^{-t}+C_2te^{-t}$$.
3. Consider a mass $$m=1$$ on a spring with spring constant $$k=4$$ oscillating on a surface with the damping constant $$c$$.Sketch the trajectories of the motion of a mass starting position $$0$$ with velocity $$1$$ for $$c=0, .1, 3, 5$$.