A First Equation: y' = y

In \( y' = y \) the slope equals the height. The solutions are the exponentials

\( y = C e^{x}. \)

The animation draws four solutions one after another; at marked points the tangent arrow shows the slope equalling the current value of \( y \).

A First Equation: y' = y
Solutions of \( y'=y \) with their tangent-direction arrows