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AP EAMCET202420 May 2024Evening ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation (x y x ) d y= (y y x -x ) d x is

Options

  1. Ax y = _e x+c
  2. By x = _e x+c
  3. Cx y = _e y+c
  4. Dy x = _e y+c

Correct answer

B. y x = _e x+c

Step-by-step solution

(x y x ) d y= (y y x -x ) d x d y d x = y y x -x x y x d y d x = y x - cosec y x Let y x =v d y d x =v+ x d v d x aligned & v+ x d v d x =v- cosec v & d v - cosec v = d x x - v d v= d x x aligned Integrating both side, we get v= x+ C y x = x+C

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