IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

paddy.dude

its homogenous form of diff equation

first of all take it as

dx/dy= x²-y²/2xy

now put x=vy

d(vy)/dy=v²y²-y²/2vy²

v+ydv/dy= v²-1/2v
ydv/dy=v²-1-2v²/2v

= -( v²+1)/2v
- 2v dv/v²+1= dy/y

integrating we get,
-log(v²+1)=log y + log c

1/v²+1= yc

but v=x/y

y²/x²+y²= yc

y=c(x²+y²)

is this the answer.........

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