Question

The differential form of the equation y2+(x−b)2=c:

• A. (A) yd2ydx2+(dy dx)2−1=0
• B. (B) yd2ydx2+dydx+1=0
• C. (C) yd2ydx2+(dydx)2+1=0
• D. (D) d2ydx2+(dy dx)2−1=0

Answer 1

Answer: (C)

(C) yd2ydx2+(dydx)2+1=0

Answer 2

Explanation:
Given,y2+(x−b)2=cThere are two constants b and c so differentiate two timesDifferentiating w.r.t xWe get,2ydydx+2(x−b)=0⇒ydydx=b−xDifferentiating again w.r.t xWe get,(dydx)2+yd2ydx2=−1⇒yd2ydx2+(dydx)2+1=0Hence, the correct option is (C).