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AP EAMCET202125 Aug 2021Morning ShiftMathematicsDifferential EquationsActual

Solve the following differential equation (x^2+1 ) d y d x +4 x y= 1 x^2+1

Options

  1. Ay (x^2-1 )^2=x+c
  2. By (x^2+1 )^2=x+c
  3. Cy (x^2+1 )^2=x^2+c
  4. Dy (x^2-1 )^2=x^2+c

Correct answer

B. y (x^2+1 )^2=x+c

Step-by-step solution

Given, differential equation aligned (x^2+1 ) d y d x +4 x y & = 1 x^2+1 d y d x + 4 x y x^2+1 & = 1 (x^2+1 )^2 IF =e^ 4 x x^2+1 d x & =e^ 2 (x^2+1 ) & = (x^2+1 )^2 aligned Solution of the differential equation is aligned & y (x^2+1 )^2= d x+c & y (x^2+1 )^2=x+c aligned

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