Weekly Math Problem! #2

Ordinary Differential Equations (ODE). For some reason, differential equations was on my mind, even when this blog was just a thought. I couldn't help thinking about a notebook 📓 that I did some ode work in years ago. I knew where the notebook was and located the specific problem that kept coming to mind. Let me tell you...when I flipped those pages, the dates were from 2010/2011. 🔟 years ago! Whoa! 😲

To solve this week's problem in completion, you need to recall the following math skills:

     ✔️  How to integrate polynomial functions 
     ✔️  Completing the square technique 
     ✔️  Solving higher order polynomial equations

Here goes WMP #2! 

Happy solving! Check back on Friday, May 15th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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Based on the nature of the derivative in the problem, the separation of variables method was used:

In finding the domain, I used both methods. What I'll do is show how to use the cubic formula to find the domain in a separate blog post. So, keep an 👁 out for that one. I knew the cubic formula existed but never used it. This week's problem was a great opportunity for that.

This solution had quite a few steps--separate the variables, integrate both functions, use the initial condition to find the constant, isolate y to find the explicit solution, then for accuracy, find the domain of that function. 🥴 *wipes perspiration from forehead* Despite the work, I do like this problem because different types of math were needed to solve in completion.

◾️ Did you arrive at the same answer I have above?? 

◾️ When was the last time you solved an ordinary differential equation??

◾️ Comment below with your responses and let me know what you thought about this week's problem.

Cheers!

The Younge Lady