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BITSAT2024MathematicsDifferential 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

Given, d y d x - y x+1 =e^ 3 x (x+1) Above is linear differential equation of form aligned & d y d x +P x=Q & IF =e^ P d x =e^ - 1 x+1 d x =e^ - (1+x) = 1 1+x aligned Solution will be aligned y IF & = Q IF d x y 1 1+x & = e^ 3 x (x+1) 1 (1+x) d x y 1+x & = e^ 3 x 3 +C^ 3 y 1+x & =e^ 3 x +C^ [ C=3 C^ ] aligned

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