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  • The general solution of x (dy/dx)+(log x)y=x^ (1/2) log x

The general solution of x (dy/dx)+(log x)y=x^ (1/2) log x

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Solution:    

               x(fracmathrmd ymathrmd x)+(log x)y=x^fraclog x2

       Rightarrow        fracmathrmd ymathrmd x+fraclog xxy=x^fraclog x2

                 I.F=e^int fraclog xxdx=e^frac(log x)^22=(e^log x)^fraclog x2=x^frac12log x.

     herefore        Solution   is      x^frac12log xcdot y=int dx

    Rightarrow                    yx^frac12log x=x+c.

Posted by

Deependra Verma

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