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AP EAMCET2011MathematicsDifferentiation

If u u(x, y)= (y+a x)-(y+a x)^2 , then it implies

Options

  1. Au_ x x =a^2 u_ y y
  2. Bu_ y y =a^2 u_ x x
  3. Cu_ x x =-a^2 u_ y y
  4. Du_ y y =-a^2 u_ x x

Correct answer

A. u_ x x =a^2 u_ y y

Step-by-step solution

On differentiating partially w.r.t. x , we get u_x= (y+a x) a-2(y+a x) a Again differentiating partially w.r.t. x , we get On differentiating partially Eq. (i) w.r.t. y , we get u_y= (y+a x)-2(y+a x) From Eqs. (ii) and (iii), we get u_ x x =a^2 u_ y y

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