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  • Slove : x+y(dy/dx)/y-x(dy/dx)=x^2+2y^2+y^4/x^2

Slove : x+y(dy/dx)/y-x(dy/dx)=x^2+2y^2+y^4/x^2

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Solution:   The given equation can be reduced to

                   xdx+ydy/ydx-xdy=(x^2+y^2)^2/x^2

                Substituting     x=rcos heta ,y=rsin heta

                 We get ,     rdr/r^2d heta =-(r^2)^2/r^2cos^2 heta Rightarrow int dr/r^3=-int sec^2 heta d heta

          Rightarrow      -1/2r^2=- an heta +c

         Substituting ,     1/2(x^2+y^2)=(y/x)+k

Posted by

Deependra Verma

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