I have two IVPs:$$\begin{align}\frac{1}{k}y'+y &= 0, ~~~y(0)=5\\\\\frac{1}{k}y'+y&=5,~~~y(0)=0\end{align}$$
The solutions are:
$$\begin{align}y(t) &= 5e^{-kt}\\y(t)&=5-5e^{-kt}\end{align}$$
[![enter image description here](https://i.stack.imgur.com/6kxWC.png)](https://i.stack.imgur.com/6kxWC.png)

Everywhere, both graphs are adding up nicely to $5$ and this is the case for *every* initil value/input. I don't think this is a coincidence but I can't see past the algebra. I feel this has to do with some symmetry or interesting physical phenomena. Any help? 

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