1.

P (L4 ) =P+ )

Answer»

dy/dx=x2+y2/x2+xy -(1)

Thus,

dy/dx is a homogeneous function.

Put y=vx in the eq.

dy/dx=v+xdv/dx

Put in eqn.(1),

v+xdv/dx=x2+y2/x2+xy

on solving, we get,

1+v/1-vdv=1/xdx

Integrating both sides we get,

-2log|v-1|-v=log|x|+c

Put v=y/x,

-2log|(y/x)-1|-y/x=log|x|+c,


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