Find the solution to

$$\frac{d y(x)}{d x}+\tanh (x) y(x)=H(x)$$

in the range $-\infty<x<\infty$ subject to $y(0)=1$, where $H(x)$ is the Heavyside function defined by

$$H(x)= \begin{cases}0 & x<0 \\ 1 & x>0\end{cases}$$

Sketch the solution.