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  • Solution of differential equation x^2 y - x^3 dy/dx =y^4 cos x is

Solution of differential equation x^2 y - x^3 dy/dx =y^4 cos x is

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Solution:  

                 x^2y-x^3fracmathrmd ymathrmd x=y^4cos x

          Rightarrow         frac1y^4fracmathrmd ymathrmd x+frac-1xfrac1y^3=-fraccos xx^3

               Put         frac1y^3=vRightarrow frac1y^4fracmathrmd ymathrmd x=-frac13fracmathrmd vmathrmd x

                     -frac13fracmathrmd vmathrmd x+frac-1xv=-fraccos xx^3

         Rightarrow       fracmathrmd vmathrmd x+frac3xv=3cos xRightarrow I.F=e^int frac3xdx=x^3

         Solution     vcdot x^3=3int cos xdxhspace0.2cm+cRightarrow frac1y^3x^3=3sin x+c.

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Deependra Verma

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