Differential Equations Flashcards

Vocabulary flashcards for key concepts in differential equations.

Differential Equation

An equation which contains derivatives of functions.

Uninhibited Growth

A real-world application of differential equations.

Newton's Law of Cooling

A real-world application of differential equations.

First Order Differential Equation

A differential equation with only the first derivative.

Second Order Differential Equation

A differential equation with the highest order derivative of the second derivative.

Initial Condition

A y-value at an arbitrary x-value, usually known as x0.

General Solution

A solution to the differential equation with some unknown constants.

Particular Solution

A fully defined solution to a differential equation.

Separable Differential Equation

A differential equation where all the variables can be separated by the = sign.

Solving Separable Equations (Step 1)

Separate the variables, ensuring differentials are in the numerator. If there's a log on one side, put all constants on the other.

Solving Separable Equations (Step 2)

Integrate. Do not forget the constant! For logs and absolute values, you can skip 'y' but should use absolute value for 'x'.

Solving Separable Equations (Step 3)

Solve for y. Be careful with the constant.

Solving Separable Equations (Step 4)

Check your work by differentiating.