1.

On putting (y)/(x)=v the differential equation (dy)/(dx)(2xy-y^(2))/(2xy-x^(2)) is transfored to

Answer»

`X(2v-1)DX=3v(v-1)dx`
`x(2v-1)dv=3v(1-v)dx`
`x(1-2v)dv=(v^(2)-2v)dx`
`(1-2v)dv=(v^(2)-2v)dx`

SOLUTION :PUTTING `y=vx` and `(dy)/(dx)=v+(dv)/(dx)`, given differetial equation reduces to
`v+x(dv)/(dx)=(2v-v^(2))/(2v-1)rArr3v(1-v)dx=x(2v-1)dv`


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