Find the general solution of the differential equation yn y

Find the general solution of the differential equation y^n - y = e^x + 1.

Solution

Solve this differential equation by using an integrating factor:
y\' - y = +1
dy / dx - y = +1
dy / dx + P(x)y = f(x)
P(x) = -1
f(x) = +1
I(x) = ^[ P(x) dx]
I(x) = ^( -1 dx)
I(x) =
I(x) = 1 /
I(x)y = I(x)f(x) dx
y / = 1/ *( +1) dx
y / = x - + C
y = (x + C)-1