Weekly Math Problem #75

1st Order ODE. This week's problem type was inspired by a student who just wanted to review and be more familiar with differential equations (of the ordinary type). I rarely get a student who needs assistance with differential equations, so you know I was excited to help the student. 🤩 These types of sessions are great for me because they force me to remember concepts and topics I don't use often. It also allows me to stay sharp. 🔪

Check out WMP #2 and WMP #47 for other problems involving differential equations. 

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

        ✔️     How to solve a 1st order, linear differential equation        

             

WMP! #75 wants us to ...

Happy solving!

Check back on Saturday, February 26th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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If you've checked out my previous differential equation WMPs, then you're aware that solutions to the problems are not short. 😒 Nonetheless, here we go... 

Once it's been identified that we're dealing with a first order, linear ordinary differential equation, it need to be put in a form that will allow us to move forward with solving it. Make the coefficient of dy/dt 1, then identify p(t) and g(t). 

Now that p(t) has been identified, we can now find the integrating factor.

The integrating factor is crucial in figuring out what the function is. 

Figuring out the function is great, but we're not done yet. We've got to deal with the constant. Now, we'll use the condition provided in the problem.

We have a function, and we have the value of the constant, C, that will yield the specified condition. Let's put it together.

And before we go, let's take a quick look at the function we just found:

** This plot was generated using Geogebra.org's calculator. **

▪️ Were you able to solve for y?
▪️ Let me know what you thought about this week's problem in the comments section. 

Thank you for solving with me this week. ✏️
We're on to WMP! #76. 🤓

Cheers!

The Younge Lady