Differential Equations for Calculus II
Here’s a list of what you must know from the material that we are covering in differential
equations.
1. Exponential Growth/Decay problems
 Set up for continuous compounding problems (i.e. start from A(t+t)-A(t) and
end with the differential equation dA/dt=rA.
 Using separation of variables to find the general solution dy/dx=ay
 Know at any given time that the solution of dy/dx=y is y=cex .
 Know how to use the exponential equation to solve continuous compounding,
bacteria growth, and radio active decay problem
2. Newton’s Law of cooling
 Know the statement leading to the differential equation.
 Know how to use separation of variables to solve dT/dt = (T(t)-Ts).
3. Salt tank problems (one tank)
 Rate in = rate out (Can use separation of variable)
 Rate in  rate out (Can not use separation of variable – will need the integrating
factor technique)
4. Falling Body problems.
 Assume that gravity is the only force (easy integration problem)
 Assume that wind resistance is also a force on the object (equation is now a
differential equation).
 Note: we will work hard on understanding how to set these problems up with
different coordinate systems.
5. Interest rate problems
 Continuous compounding
 Depositing or withdrawing continuously
6. Direction Fields
 Simple ones by hand
 Using Maple
 Equilibrium solutions
 Stability of equilibrium solutions
7. Population problems
 Use the direction field to analyze
 Solve with Maple
8. Reserve the right to add to the list!!