Ans:-
xy′=x+y
dxdy=xx+y ...1
Solving dxdy by putting y=vx
differentiating w. r. t. x
dxdy=xdxdv+vdxdx
dxdy=xdxdv+v
Putting value of dxdy and y=vx in (1)
dxdy=xx+y
xdxdv+v=xx+vx
xdxdv+v=1+v
dxdv=x1
Integrating both sides
∫dv=∫xdx
v=log∣x∣+c
putting v=xy
xy=log∣x∣+c
y=xlog∣x∣+cx
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