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Stuck on FP2 differential equation question watch

1. 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...
2. What do you get for the following:

(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...
3. (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...
Try again. I think you have made a mistake with the differentiation or substitution.
4. I get d²y/dx²=-6Asin3x-9Axcos3x ..is that correct?

EDIT: got A=2
5. Looks good.

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

EDIT: got A=2

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