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MHT CET202619 April 2026Evening ShiftMathematicsDifferential EquationsActual

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

Options

  1. A( x + y 2 ) = x + c
  2. B( x + y 2 ) = x + c
  3. C- (x + y) = x + c
  4. D(x - y) + x = c

Correct answer

B. ( x + y 2 ) = x + c

Step-by-step solution

Let x + y = v Differentiating with respect to x , we get 1 + dy dx = dv dx dy dx = dv dx - 1 Substituting this in the given differential equation: dv dx - 1 = v dv dx = 1 + v dv 1 + v = dx Integrating both sides: dv 2 ^2 ( v 2 ) = dx 1 2 ^2 ( v 2 ) dv = dx ( v 2 ) = x + c Substituting v = x + y : ( x + y 2 ) = x + c

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