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AP EAMCET2010MathematicsDifferentiation

If y= (m ⁻¹ x ) , then (1-x^2 ) y₂-x y₁ is equal to ( . Here, y_n denotes . d^n y d x^n )

Options

  1. Am^2 y
  2. B-m^2 y
  3. C2 m^2 y
  4. D-2 m^2 y

Correct answer

B. -m^2 y

Step-by-step solution

y= (m ⁻¹ x )y₁= (m ⁻¹ x ) m 1 1-x^2 where (y₁= d y d x )y₁ 1-x^2 =m (m ⁻¹ x ) y₂ 1-x^2 +y₁ 1 2 1-x^2 (-2 x)=-m (m ⁻¹ x ) m 1-x^2 ( y₂= d^2 y d x^2 ) y₂ 1-x^2 - x y₁ 1-x^2 = -m^2 1-x^2 (m ⁻¹ x ) y₂ (1-x^2 )-x y₁=-m^2 y

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