The solution of (cosx + ysinx) dx - (cosx)dy = 0 is
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(sinx+cosx)dy+(cosx-sinx)dx=0
(sinx+cosx)dy=(sinx-cosx)dx
dy/dx=sinx-cosx/sinx+cosx
Put sinx+cosx=t
Then (cosx-sinx)dx=dt
Now
dy/dx=-dt/t
Integration on both sides we got
Y=-lnt
Y=-ln(sinx+cosx) +C ANSWER
Where C is integration constan
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