The solution of (dy)/(dx) = (x + y) + (x + y), is

Put x + y = v and $1 + \dfrac{dy}{dx} = \dfrac{dv}{dx}$

Therefore, the differential equation reduces to

$\dfrac{dv}{dx} = \left(1 + \cos v\right) + \sin v = 2\cos^{2}\dfrac{v}{2} + 2sin\dfrac{v}{2}cos\dfrac{v}{2}$

$= 2\cos^{2}\dfrac{v}{2}$\left(1 + \dfrac{\tan v}{2}\right)

$⇒ ∫$\dfrac{\sec^{2}\dfrac{V}{2}}{2\left[1 + \tan \left(\dfrac{v}{2}\right)\right]}$dv = ∫ dx$

$∴ \log \left[1 + \tan \left(\dfrac{x + y}{2}\right)\right] =$ x + C$</p>$