Differential Equations, Exam 1 walkthrough (Spring 2023)

A walk-through of the solutions for Exam 1 of Differential Equations administered in Spring 2023.

0:00 Intro
1:15 1 -- Exact ODE
7:58 2 -- Linear first order (integrating factor)
12:57 3 -- General form of constant coeff. ODE
19:25 4 -- Population / find/classify critical pts
28:27 5 -- Substitution (Bernoulli OR homogeneous)
37:21 6 -- Nonhomogeneous (undetermined coeffs)

[JasonStone-bgqz]

The most chill math professor ever. This is a very helpful video.

[davide]

Professor Butler, i keep finding myself coming back to your videos every tome i need to refresh on some older topics. Your videos are on point. Thank you for all the work and effort you have put in.

[erikdurfey]

Like your explanation of the Bernoulli equation, thank you

[georgesadler]

Professor Butler, thank you for an awesome explanation and analysis of Ordinary Differential Equations, Exam 1 walkthrough for Spring 2023. The six problems on the first Exam are excellent for an Introductory course in Differential Equations. The different techniques and methods used to obtain solutions for the different problems is a great start for all students in Ordinary Differential Equations. Professor Butler in problem 5, when you integrate dx divided by x you get the ln of x +C. The correct solution is the ln of the absolute value of x +C. Please correct this small error in the video.

[LBiV]

Thank you so much for doing this! Looking forward to what exam 2 will look like

[jacksonmadison]

Like at 5:45 of this video
Undetermined Coefficients | MIT 18.03SC Differential Equations, Fall 2011

[jacksonmadison]

41:30 why isn't the Fe^x guess raised by an order of one, when the Dx^2 + Ex is?
I thought if you had a lowest order derivative of 1st order on the LHS, you had to raise all your yp guesses by one order of polynomial.

[ryancarlson]

If bob ross was a math professor <3