Solve each of the following initial value problems

(x² + y²)d x = 2xy dy, y(1) = 0

()dx = 2xy dy, y(1) = 0

It is a homogenous equation

Put y = vx

And

So,

Integrating both sides we get,

log (1 – ) = – log(x) + log c

log (1 – ) = log

put v =

Put y = 0,x = 1 in eq. (1),

1 – 0 = c

c = 1

put value of c in eq,(1),