Determine the general solution of y′=cos(x+y+1)y' = \cos(x+y+1)y′=cos(x+y+1) by using the substitution v=x+y+1v = x+y+1v=x+y+1.
x+C=ln∣sec(v)+tan(v)∣x + C = \ln|\sec(v) + \tan(v)|x+C=ln∣sec(v)+tan(v)∣
x+C=2tan(v/2)x + C = 2 \tan(v/2)x+C=2tan(v/2)
x+C=ln∣tan(v/2+π/4)∣x + C = \ln|\tan(v/2 + \pi/4)|x+C=ln∣tan(v/2+π/4)∣
x+C=sin(v)x + C = \sin(v)x+C=sin(v)