Question

Cos 3x dy/dx - 3y sin3x = 1/2sin6x + {sin}^{2} 3x

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Answer 1

Answer:

equation can be rewritten as dy/dx - 3tan3x y = sin3x + sin3x tan3x

implies integrating factor is exp(D-1(-3tan3x)) = exp(-ln sec3x) = cos3x

which implies y cos3x = D-1(sin3x cos3x + sin23x) = 1/12(-cos3x) + x/2 - 1/12(sin3x)

implies y = 1/2(x sec3x) -1/12(1+ tan3x).