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" 1."(dy)/(dx)+y cot x=sin x...

" 1."(dy)/(dx)+y cot x=sin x

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(dy)/(dx)-y cot x=csc x

Solve the equation (dy)/(dx)+y cot x=sin x

(dy)/(dx) + y cot x = sin 2x

The solution of (dy)/(dx)+y cot x =sin2x is

(dy)/(dx) = 3y cot x = sin 2x, y = 2 when x = (pi)/(2)

(dy)/(dx) - 3y cot x = sin 2x, y = 2 when x = (pi)/(2)

(dy)/(dx) = 3y cot x = sin 2x, y = 2 when x = (pi)/(2)

The I.F. of (dy)/(dx) - 3y Cot x = Sin x is

dy/dx - 3y cot x = sin 2x, given y= 2 when x = pi/ 2