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MHT CET202310 May 2023Evening ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation d y ~d x + ( 3 x^2 1+x^3 ) y= 1 x^3+1 is

Options

  1. Ay (1+x^3 )=x^3+ c , where c is a constant of integration.
  2. By (1+x^3 )=x+ c , where c is a constant of integration.
  3. Cy (1+x^3 )=x^2+ c , where c is a constant of integration.
  4. Dy (1+x^3 )=2 x+ c , where c is a constant of integration.

Correct answer

B. y (1+x^3 )=x+ c , where c is a constant of integration.

Step-by-step solution

Given differential equation is array ll & d y ~d x + ( 3 x^2 1+x^3 ) y= 1 x^3+1 & Here, P = 3 x^2 1+x^3 , Q = 1 x^3+1 & I.F. = e ^ 3 x^2 1+x^3 ~d x = e ^ (1+x^3 ) = (1+x^3 ) & Solution of the given equation is & y (1+x^3 )= 1 1+x^3 (1+x^3 ) d x+ c & y (1+x^3 )=x+ c array

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