Linear First Order ODE/y' + y = sech x

Theorem
The linear first order ODE:
 * $(1): \quad \dfrac {\d y} {\d x} + y = \sech x$

has the general solution:
 * $y = e^{-x} \paren {C + \map \ln {e^{2 x} + 1} }$

Proof
$(1)$ is a linear first order ODE with constant coefficients in the form:
 * $\dfrac {\d y} {\d x} + p y = \map Q x$

where:
 * $p = 1$
 * $\map Q x = \sech x$

Thus:

It remains to evaluate the primitive.

Let:

The result follows.