show that the given differential equation is homogeneous and solve each of them `(x^2+xy)dy=(x^2+y^2)dx`

Explanation

`(dy)/(dx)=(x^(2)+y^(2))/(x^(2)+xy)`
`implies v+x(dv)/(dx)=(x^(2)+x^(2)v^(2))/(x^(2)+x^(2)v)`
Let `y=vx`
`implies (dv)/(dx)=v+x(dv)/(dx)`
`implies x(dv)/(dx)=(1+v^(2))/(1+v)-v=(1-v)/(1+v)`
`implies (1+v)/(1-v)dv=(dx)/(x)`
`implies int((2)/(1-v)-1)dv=int(dx)/(x)+logc`
`implies -2log(1-v)-v=logx+logc`
`implies -v=logcx+2log(1-v)=log{cx(1-v)^(2)}`
`implies cx(1-v)^(2)=e^(-v)`
`implies cx(1-(y)/(x))^(2)=e^(-y//x)`
`implies c(x-y)^(2)=x*e^(-y//x)`
`implies c(x-y)^(2)*e^(y//x)=x`