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  • Suppose a solution of the differential equation (xy^3 + x^2 y^7 )dy/dx =1 satisfies the initial conditions y(1/4)=1 then the value of dy/dx when y=-1 is

Suppose a solution of the differential equation (xy^3 + x^2 y^7 )dy/dx =1 satisfies the initial conditions y(1/4)=1 then the value of dy/dx when y=-1 is

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Solution:    

                 fracmathrmd ymathrmd x=xy^3+x^2y^7

        Rightarrow           frac1x^2fracmathrmd xmathrmd y-frac1xy^3=y^7

       Rightarrow          fracd(-frac1x)dy-frac1x(y^3)=y^7     ,    I.F=e^fracy^44

      Solution  is      frac-e^fracy^44x=y^4cdot e^fracy^44-4e^fracy^44-e^frac14

      When          y=-1,x=frac14

      herefore                  fracmathrmd ymathrmd x=-frac165.

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Deependra Verma

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