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Solution of the differential equation dydx=sin(x+y)+cos(x+y) is .....

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Solution

dydx=sin(x+y)+cos(x+y)Substituex+y=vdiff.w.r.tx1+dydx=dvdxdydx=dvdx1Thegivendifferentialequationbecomesdydx=sin(x+y)+cos(x+y)dydx1=sinv+cosvdvdx=1+sinv+cosvdx=11+2tan(v2)tan2(v2)+1tan2(v2)1+tan2(v2)dxdx=1+tan2(v2)2(1+tan(v2))dvdx=sec2(v2)2(1+tanv2)dvdx=sec2(v2)2(1+tanv2)dvx=log2tan(v2)+Cx=log2tan(x+y2)+C

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