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MHT CET202520 Apr 2025Evening ShiftMathematicsDifferential EquationsActual

The particular solution of the differential equation ( dy dx )=0.5, y =1 at x=0 is

Options

  1. A( 2 x )=1
  2. B( y x-1 )=0.5
  3. C( y-1 x )=0.5
  4. D( y x )=0.5

Correct answer

C. ( y-1 x )=0.5

Step-by-step solution

The differential equation ( dy dx ) = 0.5 is solved by noting that dy dx = ⁻¹(0.5) = 3 , since ( 3 ) = 0.5 . Integrating yields y = 3 x + C . Applying the initial condition y(0) = 1 gives C = 1 , so y = 3 x + 1 . Rearranging, y - 1 x = 3 for x 0 . Taking the cosine of both sides results in ( y - 1 x ) = ( 3 ) = 0.5 , which matches option C . Final answer: C

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