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NDA2010MathematicsDifferential EquationsActual

What is the solution of the differential equation a (x d y d x +2 y )=x y d y d x ?

Options

  1. Ax^2=k y e^ y a
  2. By x^2=k y e^ y a
  3. Cy^2 x^2=k y e^ y^2 a
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

aligned & a x d y d x +2 a y=x y d y d x & or d y d x = -2 a y a x-x y & a-y y d y=-2 a d x x & or y-y=-2 a x+c & or y-y= x^ -2 a + k & or y-y= k x^ -2 a & y k x^ -2 a =y or e^y= y k x^ -2 a or k e^y=y x^ 2 a aligned

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