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Question

Differential Equations of first order and first Degree

Q. Cos(x+y) dy =dx

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Solution

Dear student
cosx+ydy=dxdydx=1cosx+yLet x+y=v.Then1+dydx=dvdxdydx=dvdx-1Putting x+y=v and dydx=dvdx-1 the given differential eq , we getdvdx-1=1cosvdvdx=1+cosvcosvcosv1+cosvdv=dxcosv1-cosv1-cos2vdv=dxcotvcosecv-cot2vdv=dxcotvcosecv-cosec2v+1dv=dx-cosecv+cotv+v=x+C On integrating-cosecx+y+cotx+y+y=C-1-cosx+ysinx+y+y=C-tanx+y2+y=Cy=tanx+y2+C
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