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y'+y=5sin(2t)

I find the integrating factor u(t)=e^t

multiply the whole function u(t)

and i get (ye^t)'=5e^tsin(2t)

I do integraton by parts on the second part and get

1/9 for the coefficents, in the calculator they don't get those coefficents! :(

very frustrating, not sure why.