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BITSAT2010MathematicsDifferential EquationsActual

What is the solution of ( d y d x +2 y=1 ) satisfying (y(0)=0 ) ?

Options

  1. A(y= 1-e^ -2 x 2 )
  2. B(y= 1+e^ -2 x 2 )
  3. C(y=1+e^x )
  4. D(y= 1+e^x 2 )

Correct answer

A. (y= 1-e^ -2 x 2 )

Step-by-step solution

( aligned & d y d x +2 y=1 d y d x =1-2 y & d y 1-2 y = d x- 1 2 |1-2 y|=x+C & at x=0, y=0 ;- 1 2 1=0+C C=0 & 1-2 y=e^ -2 x y= 1-e^ -2 x 2 aligned )

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