Find `A`and `B`so that `y=Asin3x+bcos3x`satisfies the equation`(d^2y)/(dx^2)+4(dy)/(dx)+3y=10cos3xdot`

Find `A`and `B`so that `y=Asin3x+bcos3x`satisfies the equation`(d^2y)/

1.	Find `A`and `B`so that `y=Asin3x+bcos3x`satisfies the equation`(d^2y)/(dx^2)+4(dy)/(dx)+3y=10cos3xdot`
Answer» `y=Asin3x+bcos3x` diff. with respect to x `dy/dx=Acos3x3+B(-Sin3x)3` diff with respect to x `(d^2y)/(dx^2)=-9Asin3x-9Bcos3x` `(d^2y)/(dx^2)+4dy/dx+3y=10` LHS`=-9Asin3x-9Bcos3x+12Acos3x-12Bsin3x+3Asin3x+3Bcos3x=10cos3x` `sin3x(-9A-12B+3A)+cos3x(-9B+12A+3B)=10cos3x` `12A-6B=10` `12*(-2B)-6B=10` `B=-1/3` `A=2/3`.