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solve: cot(3x)(dy/dx) -3y =cos3x + sin 3x, 0<x<90.

solve: cot(3x)(dy/dx) -3y =cos3x + sin 3x, 0

Grade:12

2 Answers

shiddhant bhattacharya
25 Points
8 years ago

the ans is y/sec3x = x/2 - 1/12( cos6x + sin6x ) + c

Rajendra Sharma
20 Points
8 years ago

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).

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