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Manipal MET2016MathematicsApplication of Derivatives

If y^ 1 / m +y^ -1 / m =2 x , then (x^2-1 ) y₂+x y₁ is equal to

Options

  1. Am^2 y
  2. B-m^2 y
  3. Cm^2 y
  4. DNone of these

Correct answer

A. m^2 y

Step-by-step solution

We have, y^ 1 / m +y^ -1 / m =2 x or y^ 1 / m + 1 y^ 1 / m =2 x aligned & or (y^ 1 / m )^2-2 x y^ 1 / m +1=0 & y^ 1 / m =x (x^2-1 ) aligned or y= [x x^2-1 ]^m y₁=m [x (x^2-1 ) ]^ m-1 [1 2 x 2 x^2-1 ] y₁= m [x (x^2-1 ) ]^m (x^2-1 ) = m y (x^2-1 ) array lr & (x^2-1 ) y₁^2=m^2 y^2 & (x^2-1 ) 2 y₁ y₂+2 x y₁^2=2 m^2 y y₁ & (x^2-1 ) y₂+x y₁=m^2 y array

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