Question

Solve : (x2+xy )dy =(x2 + y2 )dx​

Answer 1

Look,

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,

I hope it was helpful buddy!

Answer 2

Answer:

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