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Question

Solve dydx=1cos(x+y)

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Solution

dydx=1cos(x+y)

Let x+y=v
1+dydx=dvdx

dydx=dvdx1

The original differential equation becomes :
dvdx1=1cosv

dvdx=1+cosvcosv

cosvdv1+cosv=dx

cosv+111+cosvdv=x+C

dv11+cosvdv=x+C

v12cos2(v2)dv=x+C

v12sec2(v2)dv=x+C

v12tan(v2)=x+C

x+y12tanx+y2=x+C

y12tanx+y2=C

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