Unit 7: Differential Equations

Consider the differential equation [math] with initial condition [math].

Consider [math] with [math].

A population [math] satisfies the logistic equation [math] with [math].

Consider the differential equation [math].

Consider [math] with [math].

Solve the differential equation [math] with [math].

Newton's Law of Cooling states [math] where [math] is the surrounding temperature. A cup of coffee at [math] is placed in a [math] room. After 5 minutes, the temperature is [math].

Consider the autonomous equation [math].

Consider [math] with [math].

A tank initially contains 100 liters of water with 10 kg of dissolved salt. Brine with concentration 0.5 kg/L flows in at 4 L/min. The well-mixed solution drains at 4 L/min.