Math n' Stuff w/ The Younge Lady: Weekly Math Problem! #47

Sunday, April 18, 2021

Weekly Math Problem! #47

2nd Order ODE. Sometimes, topics just come to mind and I say to myself, 🤔 "Haven't done that in a while. I should do it so I don't forget." That's pretty much it. Well, sometimes I can see the problem or parts of the problem and not quite remember the name of the topic. Then I'll have a little digging to do so that I can get the name of the topic. Well, 2nd order ode (second order ordinary differential equation) is the order for this week. 😅 Specifically, we're looking at a non-homogenous equation with constant coefficients.

⚠️Many steps involved.⚠️To solve this week's problem in completion, you need to recall the following math skills:

        ✔️   How to factor a trinomial
        ✔️   How to use the method of undetermined coefficients
        ✔️   How to find derivatives

WMP! #47 says to:

Happy solving!

Check back on Friday, April 23rd for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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You can't say I didn't warn you about the many steps involved in the solution to this problem. Why did I do it? Well...because it's good practice and I want to make sure that I can remember math at this level. As I challenge my myself, I challenge you.

🧐 Let's get it!

I did my best to organize my solution and color code it so that it would be understood a little better.

The general solution to the equation can be broken down into two parts--the homogeneous solution and the particular solution.

I worked on the homogenous solution, before tackling the particular solution. Once I got bot parts, I put them together to complete the general solution to the equation.