Earlier this month, I had the privilege of leading a session at the mid-semester tutorials at Boot Class. And as many of you already know, Boot Class organizes corrosive tutorial sessions to help students catch up on their studies and address possible knowledge gaps before tests and exams.
During my session, I was taking the sophomores and juniors through MTS 205/209/315, which is a course that focus on Differential Equations. At some point, we arrived at the Existence and Uniqueness Theorem— which is a fundamental theorem used to determine whether or not a differential equation has a solution and, if it does, whether that solution is truly one of a kind.
Existence and Uniqueness Theorem
The Existence and Uniqueness Theorem is used to investigate the existence and uniqueness of the solution to a differential equation. The theorem states that if we have a differential equation of the form:
Now, I won’t drown you in complex mathematical jargon, but here’s what you need to know about what you’re seeing above.
✅ Condition (a) – Existence:
A solution exists if the function f(x, y) is continuous over a given interval. Think of it like drawing a curve without lifting your pen—no gaps, no breaks. That’s continuity! If a function behaves this way, a solution is guaranteed to exist.
✅ Condition (b) – Uniqueness:
A solution is unique if the partial derivative of f(x, y) with respect to y—that is, ∂f/∂y—is also continuous over the same interval. This condition ensures that the function doesn’t suddenly change direction or create multiple paths from the same starting point.
If these two conditions hold, then a differential equation is said to have a solution and that solution is not only solvable, it is also unique and distinct.
Now, let’s bring this idea home and make sense of it in the simplest way possible. The Existence and Uniqueness Theorem is asking us two simple but profound questions:
Does a solution exist? (Existence) – In other words, does this differential equation even have a solution, or are we just chasing a ghost?
If it exists, is it the only one? (Uniqueness) – Because an answer that isn’t unique is like a duplicated key. It’s functional but not special. You copy? 🌚
So, here’s the thing. I was supposed to give them this formal, textbook definition I just gave you. But instead, before I could stop myself, I blurted out:
“Existence and Uniqueness Theorem states that if you exist, then you’re unique!”
The entire class bursted into laughter. It felt like one of those overused inspirational quotes you'd find on a poster—complete with a soaring eagle, a golden sunset, and the words "Believe in Yourself!" 😂
Later that day, I was reminiscing on how the class went to see if there was something I could have done better when the scenario where I discussed the existence and uniqueness theorem flashed back in my memory.
But this time, I saw it differently. With a deeper, poignant reflection, I realized that my earlier statement wasn’t some wordplay. It was actually the truth:
If you exist then you're unique! The only thing that can strip away uniqueness is nonexistence. As long as you are here—breathing, thinking, and living—then you carry something no one else ever has or ever will. Your journey, your voice, your essence—they are yours and yours alone.
In Mathematics, an equation must meet certain conditions to prove that its solution exists and is unique. But in life, there’s only one condition: to exist. And because you exist, then you’re unique!
You’re unique because you exist!
You are not a redundant function or an arbitrary variable in someone else’s equation. You are not just a rearrangement of other people’s thoughts, experiences, or ambitions. Even if your path looks similar to another’s, the way you walk it is yours alone.
So listen up, my dear scholar, trying to fit into another person's mold is proof that you're yet to discover your true Identity. One of the benefits of self-discovery is that it gives you the ability to remain focused and consistent. It brings you to a point where you're no longer under pressure to look or become like others.
I hope you are aware that the more you try to become like others, the less of yourself you become? Yes! Even at the peak of “copy-cat” endeavors, the best you can become is a duplicate of the, which still makes you ingenuine. The greatest discovery you can or will ever make in life is the discovery of self and destiny. Or what is the purpose of destiny if it was not first discovered?
Remember I told you in my first letter this year that “Imitation is limitation.” It’s very true! No one ever became great by imitation. Stop being a copy of something or someone! Every good thing is a fruit of originality. Make your own impression. Be what you are. It’s the first step to becoming more than you are. And like I always say, the easiest thing to be in the world is YOU! There's no one YOUer than YOU. So let the YOU in YOU take YOU to where YOU belong!🤭
It all boils down to this: You’re unique because you exist. You have infinite potential locked up on your inside and to reach the peak of that potential, you must find YOU. You need to find your lane, fill your space then run your race.
Your existence is proof that you matter. And that’s a theorem worth believing!
Be great today and forever!💛
RECOMMENDATION CORNER
Book to Read: In Pursuit of Purpose by Dr. Myles Munroe
Song to Listen to: In Your Name by Ada Ehi
Movie to Watch: The Agency (2024)
Words of wisdom