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COMEDK202510 May 2025Morning ShiftMathematicsDifferential EquationsActual

The solution of the differential equation d y d x +y y x=0 is

Options

  1. Ax y=c
  2. Bx y=c
  3. Cy=c x
  4. Dy x=c

Correct answer

B. x y=c

Step-by-step solution

The given differential equation is dy dx + y y x = 0 . Rearranging the terms, we get dy y y = - x dx . Integrating both sides, we have dy y y = - x dx . Let u = y , then du = 1 y dy . The integral becomes du u = - x dx . This results in |u| = - | x| + C₁ . Substituting u = y , we get | y| = - | x| + C₁ . This simplifies to | y| + | x| = C₁ , which is | y x| = C₁ . Taking the exponential of both sides, | y x| = e^ C₁ = C . Thus, x y = C . Answer: x y=c

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