dydx=sin(x+y)+cos(x+y)Substituex+y=vdiff.w.r.tx1+dydx=dvdxdydx=dvdx−1Thegivendifferentialequationbecomesdydx=sin(x+y)+cos(x+y)dydx−1=sinv+cosvdvdx=1+sinv+cosvdx=11+2tan(v2)tan2(v2)+1−tan2(v2)1+tan2(v2)dxdx=1+tan2(v2)2(1+tan(v2))dvdx=sec2(v2)2(1+tanv2)dv∫dx=∫sec2(v2)2(1+tanv2)dvx=log∣∣2tan(v2)∣∣+Cx=log∣∣2tan(x+y2)∣∣+C