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COMEDK20269 May 2026Morning ShiftMathematicsDifferential EquationsActual

The solution of dy = x (2 - y cosec x) dx where y = 2 when x = 4 is

Options

  1. Ay = ( x 2 ) + ( x 2 )
  2. By = x + 1 2 cosec x
  3. Cy x = 1 2 2x
  4. Dy = 1 2 x + 2 ( x 2 )

Correct answer

B. y = x + 1 2 cosec x

Step-by-step solution

The given differential equation can be rewritten as: dy dx = 2 x - y x cosec x dy dx + y x = 2 x This is a linear differential equation of the form dy dx + P y = Q , where P = x and Q = 2 x . The integrating factor (IF) is: IF = e^ x dx = e^ ( x) = x Multiplying the differential equation by the integrating factor and integrating both sides: y x = 2 x x dx + C y x = 2x dx + C y x = - 2x 2 + C Given y = 2 when x = 4 : 2 ( 4 ) = - ( /2) 2 + C 2 ( 1 2 ) = 0 + C C = 1 Substituting C = 1 back into the equation: y x = 1 -

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