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MHT CET202620 April 2026Morning ShiftMathematicsDifferential EquationsActual

If x is an integrating factor of the differential equation dy dx + Py = Q , then P can be

Options

  1. A2 2x
  2. B2x
  3. C2x
  4. D2 2x

Correct answer

D. 2 2x

Step-by-step solution

The integrating factor of the linear differential equation dy dx + Py = Q is given by e^ P dx . Given that the integrating factor is x , we have: e^ P dx = x Taking the natural logarithm on both sides: P dx = ( x) Differentiating both sides with respect to x : P = d dx ( ( x)) P = 1 x ^2 x P = x x 1 ^2 x P = 1 x x P = 2 2 x x P = 2 2x P = 2 2x Answer: 2 2x

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