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BITSAT2020MathematicsDifferential EquationsActual

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

Options

  1. Ay=(x+1) e^ 3 x +c
  2. B3 y=(x+1)+e^ 3 x +c
  3. C3 y x+1 =e^ 3 x +c
  4. Dy e^ -3 x =3(x+1)+c

Correct answer

C. 3 y x+1 =e^ 3 x +c

Step-by-step solution

The given equation is d y d x - y x+1 =e^ 3 x (x+1) I.F. =e^ - 1 x+1 d x =e^ - (x+1) = 1 x+1 The solution is y ( 1 x+1 )= e^ 3 x (x+1) 1 x+1 d x+a y x+1 = e^ 3 x d x+a= e^ 3 x 3 +a 3 y x+1 =e^ 3 x +c, c=3 a

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