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COMEDK2022MathematicsDifferential Equations

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

Options

  1. Ay x=c
  2. Bx y=c
  3. C(x y)=c
  4. D(y x)=c

Correct answer

B. x y=c

Step-by-step solution

The given differential equation is x dy dx = y . Separating the variables, we get dy y = dx x . This simplifies to y , dy = dx x . Integrating both sides, we have y , dy = dx x . The integral of y is | y| or - | y| . Thus, - | y| = |x| + C . Rearranging the terms, |x| + | y| = -C . Using the property of logarithms, |x y| = C' , where C' = -C . Taking the exponential of both sides, x y = e^ C' = c . Answer: x y=c

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