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KCET2012MathematicsDifferential Equations

Solution of e^ d y / d x =x when x=1 and y=0 is

Options

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

Correct answer

D. y=x( x-1)+1

Step-by-step solution

Given, e^ d y / d x =x Taking logarithm on both sides, we get aligned e^ d y / d x &= x d y d x &= x d y &= x d x aligned On integrating, we get aligned & aligned dy &= xdx &= x 1 dx - [ d dx x 1 dx ] dx &= x x - 1 x x dx &= x x - dx &= x x - x y &= x ( x -1)+ C when x &=1 and y =0 0=1( 1-1)+ C aligned aligned array ll & 0=(0-1)+C & C=1 array Eq . (i) becomes y=x( x-1)+1

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