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AP EAMCET2005MathematicsDifferential Equations

If d y d x = y+x y x x , then y x is equal to

Options

  1. Ac x^2
  2. Bc x
  3. Cc x^3
  4. Dc x^4

Correct answer

B. c x

Step-by-step solution

Given that This is a homogeneous differential equation. Put y=v x and d y d x =v+x d v d x From Eq. (i), v+x d v d x = v x+x ( v x x ) x x d v d x =v+ v-v v d v= d x x On integrating both sides, we get aligned & & v & = x+ c & & v & =x c & & y x & =x c aligned

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