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AP EAMCET202017 Sep 2020Morning ShiftMathematicsDifferential EquationsActual

Find the solution of the differential equation ( (e^ y-x ) d y= (e^x-e^y ) d x )

Options

  1. A(e^y e^x=e^ 2 x -e^ x^2 +c )
  2. B(e^y e^x=e^x e^ e^x -e^ e^x +c )
  3. C(e^y e^ e^x =e^x e^ e^x -e^ e^x +c )
  4. D(e^ e^y e^x=e^x e^ e^x -e^ e^x +c )

Correct answer

C. (e^y e^ e^x =e^x e^ e^x -e^ e^x +c )

Step-by-step solution

( (e^ y-x ) d y= (e^x-e^y ) d x ) ( aligned & e^y d y d x =e^ 2 x -e^x e^y & e^y d y d x +e^x e^y=e^ 2 x aligned ) Let ( e^y=z e^y d y d x = d z d x d z d x +e^x z=e^ 2 x ) ( IF =e^ e^x d x =e^ e^x ) ( ) Solution is (Z e^ e^x = e^ 2 x e^ e^x d x+c ) Let ( e^x=u ) ( aligned & & e^x d x=d u & Z e^ e^x & = u e^u d u+c=u e^u-e^u+c & e^y e^ e^x & =e^ e^x (e^x-1 )+c aligned )

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