video1.0<iframe src="https://www.loom.com/embed/a38961cb4a1841e18a720014afe793d2" frameborder="0" width="1838" height="1378" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>13781838Loomhttps://www.loom.com13781838https://cdn.loom.com/sessions/thumbnails/a38961cb4a1841e18a720014afe793d2-17ced1b3f6f08eeb.gif4108.666667I talked through several long first order differential equation questions, focusing on how to rearrange them into the integrating factor form before solving. For the salt tank model, I derived an equation for salt amount and found 27 grams after 10 minutes, then solved for the time when concentration reaches 0.9, getting 115 minutes, and noted mixing instantaneously is a key assumption. For the pond pollutant model I set up dx dt equals 50 minus 4x over 200 plus t, giving 370 grams after 8 days. I also solved a bacteria population model and a paint mixing model, and evaluated modeling error, for example predicting 7 seconds versus 9 seconds for equal red and blue. There was no direct action requested from viewers.