Math, asked by aksyrt, 11 months ago

solve this problem by the method of separation of variable!!!!!!

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Answered by vishalkumar2806
1

 \frac{dy}{dx}  = cos(x + y) \\ put \: x + y = u \\ diff \: on \: both \: side \: wrt \:  \\  1 +  \frac{dy}{dx}  = \frac{du}{dx}  \\

 \frac{dy}{dx}  = 1 -  \frac{du}{dx}  \\ put \: in \: 1 \\ 1 -  \frac{du}{dx} = cos \: \: u \\

 \frac{du}{dx}  = 1 - cos \: u \\ dx \:  = \:  \frac{du}{1 - cos \: u} \\ rationlise \: and \: then \: seperate   \\ integrtion \: on \: both \: side \\  x =  - cot \: u - cosec \: u \:  + c \\ put \: u = x + y \\ x =  - cot \: (x + y) \:  - cosec(x + y) \:  + c

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