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Solution of diffrential equation (x^2-xy)dy = (xy+y^2)dx   is 

  • Option 1)

    ln (xy) - y/x= C

  • Option 2)

    ln (xy) + x/y= C

  • Option 3)

    ln (xy) + y/x= C

  • Option 4)

    ln (xy) - x/y= C

 

Answers (1)

best_answer

As we have learned

General form of Variable Separation -

d\left ( log xy \right )=\frac{ydx+xdy}{xy}

-

 

 Given equation can be written as 

x^2dy - xydx = xydy+ y^2dx

\Rightarrow x( xdy-ydx)= y (xdy+ydx)

\Rightarrow x( xdy-ydx)/y= (xdy+ydx)

dividing both sides by xy we get 

\Rightarrow ( xdy-ydx)/y^2 = (xdy+ydx)/xy

\Rightarrow -(( xdy-ydx)/y^2 )= d(lnxy)

\Rightarrow -(d(x/y))= d(lnxy)

On integrating both sides we get 

\Rightarrow -x/y= lnxy+C

\Rightarrow ln (xy)+ x/y = C

 

 

 

 

 

 


Option 1)

ln (xy) - y/x= C

Option 2)

ln (xy) + x/y= C

Option 3)

ln (xy) + y/x= C

Option 4)

ln (xy) - x/y= C

Posted by

gaurav

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