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Manipal MET2013MathematicsDifferential Equations

The slope of the tangent at (x, y) to a curve passing through (1, 4 ) is given by y x - ^2 ( y x ) then the equation of the curve is

Options

  1. Ay= ⁻¹ ( c x )
  2. By=x ⁻¹ ( x c )
  3. Cy=x ⁻¹ ( c x )
  4. DNone of these

Correct answer

C. y=x ⁻¹ ( c x )

Step-by-step solution

We have, d y d x = y x - ^2 ( y x ) Putting y=v x , so that d y d x =v+x d v d x v+x d v d x =v- ^2 v d v ^2 v =- d x x ^2 v d v=- 1 x d x on integration, we get aligned v & =- x+ c ( y x ) & =- x+ c aligned this passes through (1, / 4) therefore, 1= c So; ( y x )=- x+1 ( y x )=- x+ c y=x ⁻¹ ( c x )

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