Question

dy/dx=arctan (x+y)

Answer 1

Put x+y=t
Now, dt/dx=d(x+y)/dx
=1+dy/dx
Therefore, dy/dx=dt/dx-1
Eqn, becomes: dt/dx-arctan(t)=1
Now, it's a Linear Differential Equation

Answer 2

it forces u to integrate something hard
http://www.wolframalpha.com/input/?i=%5Cint+1%2F%281%2Barctan%28x%29%29

Answer 3

dy/dx=arctan (x+y)

tan(y') = x + y

sec^2(y') y'' = 1 + y'

y'' = 1 + tan'(x+y)
------------------
1 + tan^2(tan'(x+y))

hmmm

Answer 4

@kutabs