solve the Diffretial equation, y-x(dy/dx) =x+y(dy/dx) .
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Answer:
Re-arranging the differential equation gives us
dx
dy
=
x
y
+
x
y
2
+x
2
dx
dy
=
x
y
+
x
2
y
2
+x
2
Let y=vx, then
dx
dy
=v+
dx
xdv
Hence
v+
dx
xdv
=v+
1+v
2
dx
xdv
=
1+v
2
∫
1+v
2
dv
=∫
x
dx
ln(v+
1+v
2
)=lnx+C
Or
ln(y+
x
2
+y
2
)−lnx=lnx+c
ln(y+
x
2
+y
2
)=2lnx+c
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