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JEE Main2008MathematicsDifferential EquationsActual

The solution of the differential equation d y d x = x+y x satisfying the condition y(1)=1 is

Options

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

Correct answer

D. y=x x+x

Step-by-step solution

y=v x aligned & d y d x =v+x d v d x & v+x d v d x =1+v & d v= d x x & v= x+c & y x = x+c aligned Since, y(1)=1 , we have y=x x+x

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