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BITSAT2024MathematicsDifferential EquationsActual

If d y d x -y _e 2=2^ x ( x-1) _e 2 , then y

Options

  1. A2^ x +c 2^x
  2. B2^ x +c 2^x
  3. C2^ x +c 2^ -x
  4. D2^ x +c 2^ -x

Correct answer

A. 2^ x +c 2^x

Step-by-step solution

d y d x -y _e 2=2^ x ( x-1) _e 2 This is linear differential equation I.F. =e^ - _e 2 d x =e^ -x _e 2 =2^ -x then general Solution is y 2^ -x = 2^ -x 2^ x ( x-1) _e 2 d x+c Now let x-x=t ( x-1) d x=d t aligned & y 2^ -x = _e 2 2^t d t+c & y 2^ -x =2^t+c & y=2^ x+t +c 2^x & y=2^ x +c 2^x aligned

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