Trig derivatives problem  TOPIC_SOLVED

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Trig derivatives problem

Postby Andromeda on Tue Nov 16, 2010 1:38 am

Find constants A and B such that the function y = Asin(x) + Bcos(x) satisfies the differential equation y" + y' - 2y = sin(x)

I can find the derivatives just fine, but I'm not sure where to go in order to solve for A or B.
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Re: Trig derivatives problem

Postby Martingale on Tue Nov 16, 2010 2:51 am

Andromeda wrote:Find constants A and B such that the function y = Asin(x) + Bcos(x) satisfies the differential equation y" + y' - 2y = sin(x)

I can find the derivatives just fine, but I'm not sure where to go in order to solve for A or B.



plug your derivatives into the equation and solve for A and B. If you want more help show what you have so far.
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Re: Trig derivatives problem

Postby Andromeda on Tue Nov 16, 2010 6:36 pm

y'(x) = Acosx - Bsinx
y"(x) = -Asinx - Bcosx

(-Asinx - Bcosx) + (Acosx - Bsinx) - 2(Asinx + Bcosx) = sinx

From here I'm not sure how to solve for A or B since there are 2 unknowns and only 1 equation :confused:
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Re: Trig derivatives problem  TOPIC_SOLVED

Postby Martingale on Tue Nov 16, 2010 6:40 pm

Andromeda wrote:y'(x) = Acosx - Bsinx
y"(x) = -Asinx - bcosx

(-Asinx - Bcosx) + (Acosx - Bsinx) - 2(Asinx + Bcosx) = sinx

From here I'm not sure how to solve for A or B since there are 2 unknowns and only 1 equation :confused:


Isolate the sines and cosines

you should get something like




or another way to look at it



then

where are functions A and B.

solve this system of two equations and 2 unknowns
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