My question is quite simple, but the more I look at it, the less content I am. My question is how to do a RK4 method for $y'=y$. At first I would assume the following:

$$k\_1=y\_n$$

$$k\_2=y\_n+\frac{h}{2}k\_1$$

and right here you can actually start to see part of the issue that I have, namely that it seems in the second equation we are adding apples and oranges since $h$ is not unitless. Nonetheless, in continuing onward:

$$k\_3=y\_n+\frac{h}{2}k\_2$$

$$k\_4=y\_n+h\ k\_3$$

and now put all together,

$$y\_{n+1}=y\_n+\frac{h}{6}(k\_1+2k\_2+2k\_3+k\_4)$$.

So for all of these it seems as though we are adding apples and oranges (my case is exactly this pretty much, finding position by taking the derivative of the velocity). Furthermore, in this last equation to solve for the next step, $y'$ does not appear in it at all, which to me seems really weird (not right at all). To clarify why I am confused on this point, is because normally the first step is an Euler Step, in which case the whole thing put together would look like:

$$y\_{n+1}=y\_n+h\ y'\_{n}$$

Part of the reason I bring this up is because I am given $y'$ and need to now map it's derivative (just like the above Euler Method). I have used RK4 many times on more complicated equations, but for some reason this one just doesn't seem quite right. Thanks!