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Introduction
A central goal in differential equations is learning how to find their solutions. In fact, most problems you’ll encounter begin with a familiar prompt:
“Find the solution to the following differential equation.”
This "solve and move on" mindset can sometimes obscure a deeper, more important question:
“What does it actually mean to be a solution to a differential equation?”
In algebra, a solution is any
value that “satisfies” the algebraic equation. In contrast, a solution to a differential equation is any
function that “satisfies” the differential equation. Understanding what it means for a function to satisfy a differential equation is the first step toward understanding its solutions.
