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# Differential Equations

# Differential Equations Exercises

#### Differential Equations and Their Solutions

A differential equation (d.e.) is any equation that has one or more derivative in it. These can be first derivatives, second derivatives...whatever.Sample ProblemThe following are differential equa...

#### Word Problems

We can use differential equations to talk about things like how quickly a disease spreads, how fast a population grows, and how fast the temperature of cookies rises in an oven. Translating between...

#### Slope Fields

If you build it, they will come.Consider the first-order differential equationWe can't solve this d.e. by thinking backwards, but we can still think about how a solution to this d.e. would behave....

#### Slopes (Again)

We know that the slope of a line is given byor bySince y is usually the dependent variable and x is usually the independent variable, you may also seeorThe symbol Δ is the Greek capital letter "De...

#### Tangent Line Approximations (Again)

Tangent line approximation can also be called local linearization, linear approximation, and probably a bunch of other names. The important thing is that you're using a line to approximate a curve....

#### The Scoop on Euler

Euler's Method is a bunch of tangent line approximations stuck together. The basic idea is that you start with a differential equation and a point. You do a tangent line approximation to get a new...

#### Accuracy and Usefulness of Euler's Method

Things to remember about Euler's Method:Euler's Method gives only approximate values unless the function happens to be a straight line, in which case Euler's Method gives exact values of the functi...