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AP EAMCET · Maths · Differentiation

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

  1. A \(u_{x x}=a^2 \cdot u_{y y}\)
  2. B \(u_{y y}=a^2 u_{x x}\)
  3. C \(u_{x x}=-a^2 \cdot u_{y y}\)
  4. D \(u_{y y}=-a^2 u_{x x}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(u_{x x}=a^2 \cdot u_{y y}\)

Step-by-step Solution

Detailed explanation

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