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AP EAMCET2007MathematicsDifferential Equations

The solution of d y d x = y^2 x y-x^2 is

Options

  1. Ae^ y / x =k x
  2. Be^ y / x =k y
  3. Ce^ x / y =k x
  4. De^ -y / x =k y

Correct answer

B. e^ y / x =k y

Step-by-step solution

Given, d y d x = y^2 x y-x^2 Put y=v x array rlrl & d y d x & =v+x d v d x & & v+x d v d x & = v^2 x^2 v x^2-x^2 & x d v d x & = v^2 v-1 -v & & x d v d x & = v v-1 & & (1- 1 v ) d v & = d x x & v- v & = x+ k & y / x & = x k y x array array llrl & y x & = y k & e^ y / x & =y k array

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