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AP EAMCET2007MathematicsDifferentiation

x= , y= 5 (1-x^2 ) d^2 y d x^2 -x d y d x is equal to

Options

  1. A-5 y
  2. B5 y
  3. C25 y
  4. D-25 y

Correct answer

D. -25 y

Step-by-step solution

Given, x= , y= 5 d x d =- , d y d =5 5 aligned & d y d x = d y / d d x / d =- 5 5 & d^2 y d x^2 = d d x ( d y d x )= d d ( d y d x ) d d x & = d d ( -5 5 ) 1 - & = ( 5 25+5 5 ^2 ) 1 - & =- 25 5 ^2 - 5 5 ^3 aligned Now, aligned & (1-x^2 ) d^2 y d x^2 -x d y d x &= (1- ^2 ) ( -25 5 ^2 - 5 5 ^3 ) &- ( -5 5 ) &= ^2 ( -25 5 ^2 - 5 5 ^3 ) &+ 5 5 &=-25 5 - 5 5 + 5 5 &=-25 5 &=-25 y aligned

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