Question

The solution of the equation $\frac { d y } { d x } = ( x + y ) ^ { 2 }$ is

• A. $x + y + \tan ( x + c ) = 0$
• B. $x - y + \tan ( x + c ) = 0$
• C. $x + y - \tan ( x + c ) = 0$
• D. None of these

Answer 1

Answer: (C)

$x + y - \tan ( x + c ) = 0$

Answer 2

Put $x + y = v$ and $1 + \frac { d y } { d x } = \frac { d v } { d x }$

⇒ $\frac { d v } { d x } = v ^ { 2 } + 1$ ⇒$\frac { d v } { v ^ { 2 } + 1 } = d x$

On integrating, we getd

$\tan ^ { - 1 } v = x + c$or $v = \tan ( x + c )$ ⇒ $x + y = \tan ( x + c )$ .