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AP EAMCET2011MathematicsDifferential Equations

The solution of the differential equation d y d x = y x + (y / x) ^ (y / x) is

Options

  1. Ax ( y x )=k
  2. B( y x )=k x
  3. Cy ( y x )=k
  4. D( y x )=k y

Correct answer

B. ( y x )=k x

Step-by-step solution

Given, d y d x = y x + ( y x ) ^ ( y x ) Put y=v x d y d x =v+x d v d x aligned & v+x d v d x =v+ (v) ^ (v) & ^ (v) (v) d v= d x x & aligned On integrating, we get gathered (v)= x+ k (v)=k x ( y x )=k x gathered

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