- #1

chwala

Gold Member

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- Homework Statement
- see attached

- Relevant Equations
- understanding of homogenous and inhomegenous approach in solving ode's

My interest is on the highlighted (In Red). Otherwise the other steps are clear.

We have on that part of the problem,

##(-p\sin t -q\cos t)-12(p\cos t -q \sin t)+36p\sin t +36q\cos t = 37 \sin t + 0 \cos t##

Ah I just realized we are solving a simultaneous equation for ##p## and ##q## !

My problem was on how to get,

##-q-12p+36q =0##

Clear now.

Cheers if there is another approach to the problem. Laplace? I may need to refresh on it.

I now have (using laplace);

##s^2 \bar y -12(s\bar y -1) +36 \bar y = \dfrac {37}{s^2+1}##

##\bar y = \dfrac{37}{(s^2+1)(s-6)^2} - \dfrac{12}{(s-6)^2}## will proceed later.

We have on that part of the problem,

##(-p\sin t -q\cos t)-12(p\cos t -q \sin t)+36p\sin t +36q\cos t = 37 \sin t + 0 \cos t##

Ah I just realized we are solving a simultaneous equation for ##p## and ##q## !

My problem was on how to get,

##-q-12p+36q =0##

Clear now.

Cheers if there is another approach to the problem. Laplace? I may need to refresh on it.

I now have (using laplace);

##s^2 \bar y -12(s\bar y -1) +36 \bar y = \dfrac {37}{s^2+1}##

##\bar y = \dfrac{37}{(s^2+1)(s-6)^2} - \dfrac{12}{(s-6)^2}## will proceed later.

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