{"type":"video","version":"1.0","html":"<iframe src=\"https://www.loom.com/embed/f30adeaf1f2d425aa85202729c6f8427\" frameborder=\"0\" width=\"1838\" height=\"1378\" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>","height":1378,"width":1838,"provider_name":"Loom","provider_url":"https://www.loom.com","thumbnail_height":1378,"thumbnail_width":1838,"thumbnail_url":"https://cdn.loom.com/sessions/thumbnails/f30adeaf1f2d425aa85202729c6f8427-34ae22514322f01d.gif","duration":3890.689889,"title":"9FM0 CP2 - Set 10C - Coupled 1st Order DEs V2","description":"In this Loom I worked through several differential equation problems step by step, showing how to rearrange and differentiate to eliminate variables, then solve the resulting auxiliary equations. For the antibiotics model I derived the general tissue concentration y, found constants using y at t equals 0, and got an eventual level of about 196.9, which sits in the accepted range. For the crayfish system I solved for w and used w near zero to find t equals about 1.165 years after t equals 0, giving a limitation about populations going negative. I also completed a fox and rabbit model, finding when rabbits die out at about year 2019 and the fox count at about 3750. There was no explicit action requested from viewers."}