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MHT CET202618 April 2026Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation x x dy dx + (x x + x)y = x is

Options

  1. Ax x + y x = c
  2. By x + x x = c
  3. Cxy x - x = c
  4. Dxy x + x = c

Correct answer

D. xy x + x = c

Step-by-step solution

The given differential equation is x x dy dx + (x x + x)y = x Observing the left hand side, it can be rewritten using the product rule of differentiation: x x dy dx + y d dx (x x) = x d dx (xy x) = x Integrating both sides with respect to x : d dx (xy x) dx = x dx xy x = - x + c xy x + x = c Answer: xy x + x = c

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