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MHT CET202012 Oct 2020Morning ShiftMathematicsDifferential EquationsActual

The solution of differential equation x² d y d x =y²+x y is

Options

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

Correct answer

A. x y + |x|=c

Step-by-step solution

We have x² d y d x =y²+x y array l d y d x = y²+x y x² ...(1) Put y=u x d y d x =u+x d u d x array Equation (1) becomes u+x d u d x = u² x²+x(u x) x² u+x d u d x =u²+u array l x du dx = u ² du u ² = dx x -1 u = | x |+ c ₁ - x y = | x |+ c ₁ x y + | x |= c array

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