I just started to learn about Differential equations, I've been reading about families of curves, but I I just got stuck with this problem. I have been Trying to solve it, I have come to find the line for a specific point as (0, 1), which gives me as a result g(x) = ex, but I don't know how to obtain a function that can describe all the lines tangents at all points of $e^x$.
Question: Find the family of straight lines that are tangents to $e^x$. Find the differential equation that satisfies those lines.