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KCET2012MathematicsDifferential Equations

If m ⁻¹ x= _ e y , then (1-x² ) y^ -x y^ is equal to

Options

  1. Am ² y
  2. B-m² y
  3. C2 y
  4. D-2 y

Correct answer

A. m ² y

Step-by-step solution

aligned & Given, m ⁻¹ x = _ e y & y = e ^ m ⁻¹ x aligned On differentiating w.r.t. x , we get y^ =e^ m ⁻¹ x m 1-x² 1- x ² y ^ = my On squaring both sides, we get (1-x² ) y^ 2 =m² y² Again differentiating, we get aligned & (1-x² ) 2 y^ y^ +y^ 2 (-2 x)=m² 2 y y^ & (1-x² ) y^ -x y^ =m² y aligned

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