SOLUTION: please solve the differential equation : dy/dx*tany = sin(x+y) +sin(x-y)

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Question 963816: please solve the differential equation :
dy/dx*tany = sin(x+y) +sin(x-y)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28dy%2Fdx%29%2Atany+=+sin%28x%2By%29+%2Bsin%28x-y%29
%28dy%2Fdx%29%2Atany+=+2sin%28x%29cos%28y%29
%28sin%28y%29%2Fcos%5E2%28y%29%29dy=2sin%28x%29dx
Use a substitution,
z=cos%28y%29
dz=-sin%28y%29%2Ady
So then,
-dz%2Fz%5E2=2sin%28x%29dx
1%2Fz=-2cos%28x%29%2BC
1%2Fcos%28y%29=-2cos%28x%29%2BC
highlight%28sec%28y%29=C-2cos%28x%29%29