Question

The differential equation of the family of curves represented by the equation $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$ is

• A. $x + y \frac { d y } { d x } = 0$
• B. $y \frac { d y } { d x } = x$
• C. $y \frac { d ^ { 2 } y } { d x ^ { 2 } } + \left( \frac { d y } { d x } \right) ^ { 2 } = 0$
• D. None of these

Answer 1

Answer: (A)

$x + y \frac { d y } { d x } = 0$

Answer 2

Given equation $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$. Differentiate it w.r.t. x,

we get $2 x + 2 y \frac { d y } { d x } = 0$ ⇒ $x + y \frac { d y } { d x } = 0$.