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Stuck on FP2 differential equation question

Find the value for A for which Axcos3x is a particular integral of the differential equation
d²y/dx² +9y=-12sin3x

I've tried subbing in y=Axcos3x into the LHS but that gives me sin3x and cos3x terms both with A in them so I can't compare coefficients... :s-smilie:
What do you get for the following:

d2dx2(Axcos⁡(3x)) \dfrac{d^2}{dx^2} (A x \cos(3x) )

Original post by bobbricks
Find the value for A for which Axcos3x is a particular integral of the differential equation
d²y/dx² +9y=-12sin3x

I've tried subbing in y=Axcos3x into the LHS but that gives me sin3x and cos3x terms both with A in them so I can't compare coefficients... :s-smilie:
Original post by bobbricks
Find the value for A for which Axcos3x is a particular integral of the differential equation
d²y/dx² +9y=-12sin3x

I've tried subbing in y=Axcos3x into the LHS but that gives me sin3x and cos3x terms both with A in them so I can't compare coefficients... :s-smilie:


Try again. I think you have made a mistake with the differentiation or substitution.
Reply 3
Avatar for bobbricks
bobbricks
OP
19
I get d²y/dx²=-6Asin3x-9Axcos3x ..is that correct?

EDIT: got A=2
(edited 9 years ago)
Looks good.

Original post by bobbricks
I get d²y/dx²=-6Asin3x-9Axcos3x ..is that correct?

EDIT: got A=2

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