Differential Equations, Exam 1 walkthrough (Spring 2024)

A walk-through of the solutions for Exam 1 of Differential Equations administered in Spring 2024.

0:00 Intro
0:39 1 -- Exact ODE
7:49 2 -- Linear first order (integrating factor)
14:45 3 -- Substitution (matching problem)
31:51 4 -- Logistic equation problem
43:34 5 -- Finding soln. from characteristic polynomial
52:17 6 -- Nonhomogeneous (undetermined coeffs)

[jacksonmadison]

Wow, the last problem is so much quicker with LaPlace 54:00

[jacksonmadison]

37:15 I like to use
P' = kP(1 - P/M)
and then Analytic solution A = (M - Pinitial) / Pinitial
P(t) = M / (1 + Ae^(-kt))
same thing, just dividing everything by Pinitial