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COMEDK20269 May 2026Morning ShiftMathematicsDifferential EquationsActual

The particular solution of the equation ( dy dx ) = a , where a R and y = 2 when x = 0 is

Options

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

Correct answer

C. ( y-2 x ) = a

Step-by-step solution

Given differential equation is ( dy dx ) = a dy dx = ⁻¹(a) Integrating both sides with respect to x : dy = ⁻¹(a) dx y = x ⁻¹(a) + C Substituting y = 2 when x = 0 : 2 = 0 + C C = 2 Substituting C = 2 in the general solution: y = x ⁻¹(a) + 2 y - 2 x = ⁻¹(a) ( y - 2 x ) = a Answer: ( y-2 x ) = a

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