1.

`(x^(2)-y^(2))dx+2xy dy=0`

Answer» `2xy dy = (y^(2)-x^(2))dx`
`implies (dy)/(dx)=(y^(2)-x^(2))/(2xy)`
`implies v+x(dv)/(dx)=(v^(2)x^(2)-x^(2))/(2x^(2)v)`
माना `y = vx implies (dy)/(dx)=v+x(dv)/(dx)`
`implies x(dv)/(dx)=(v^(2)-1)/(2v)-v=(-(1+v^(2)))/(2v)`
`implies (2v)/(1+v^(2))dv=-(dx)/(x)`
`implies int(2v)/(1+v^(2))dv=-int(dx)/(x)+logc`
`implies log(1+v^(2))=-logx+logc`
`implies 1+v^(2)=(c)/(x) implies x^(2)+v^(2)x^(2)=cx`
`implies x^(2)+y^(2)=cx`


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