Vocab

Click to reveal content**Definition: Ordinary Differential Equation (ODE):** An equation that contains one or more derivatives of an unknown function.
Click to reveal content**Definition: Partial Differential Equation (PDE):** An equation that contains one or more partial derivatives of an unknown function of two or more variables.
Click to reveal contentDefinition: Explicit form of a differential equation: y' = f(x,y)

Solution #

Click to reveal contentDefinition: General Solution**: Solutions to differential equations with arbitrary constant(s) c.
Particular SolutionA solution to a differential equation without arbitrary constants.
## Practice 2
Click to reveal contentDefinition: Initial Value Problem**: An ODE with an initial value.

**Import

Click to reveal contentDefinition: Direction Field**: A description of the rate of change on the possible values of a function.

See the book.

Click to reveal contentDefinition: Separable ODE**: Equations that are of the form or can be manipulated into the form \\(g(y)y' = f(x)\\).

Homogeneou #

Click to reveal contentDefinition: Differential: Given a function has continuous partial derivatives, the differential is** \\(du = \frac{\partial u}{\partial x}dx + \frac{\partial u}{\partial y}dy\\)
Exact Differential EquationM(x,y) + N(x,y)y' = 0** This is equivalent to \[ \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x} \] .