Ordinary Differential Equations (ODEs)

ODEs are equations that relate a function and its derivatives. They are solved for a specific function with respect to one variable.

What is an ordinary differential equation?

"An ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable."

How does an ordinary differential equation differ from other differential equations?

"The term 'ordinary' is used in contrast with partial differential equations which may be with respect to more than one independent variable."

What does the unknown in an ordinary differential equation consist of?

"Its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions."

How many independent variables does an ordinary differential equation depend on?

"[An ODE] is dependent on only a single independent variable."

What is the essential characteristic of an ordinary differential equation?

"Its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions."

Are ordinary differential equations limited to one unknown function?

"Its unknown(s) consists of one (or more) function(s)..."

How is an ordinary differential equation classified?

"It is a differential equation dependent on only a single independent variable."

What type of equations are grouped under partial differential equations?

"Partial differential equations which may be with respect to more than one independent variable."

Can partial differential equations have multiple unknown functions?

"[An ODE's] unknown(s) consists of one (or more) function(s)..."

What is the purpose of using the term "ordinary"?

"The term 'ordinary' is used in contrast with partial differential equations..."

Do ordinary differential equations involve derivatives?

"[An ODE's unknown(s)] involves the derivatives of those functions."

Is it possible for an ordinary differential equation to involve more than one derivative?

"[An ODE's unknown(s)] involves the derivatives of those functions."

Does an ordinary differential equation require multiple independent variables?

"[An ODE] is dependent on only a single independent variable."

Are ordinary differential equations common in mathematics?

"Yes, in mathematics, an ordinary differential equation..."

What makes ordinary differential equations different from other types of equations?

"[ODEs] may be with respect to more than one independent variable."

What determines the number of unknown functions in an ordinary differential equation?

"[ODEs] consists of one (or more) function(s)."

How are ordinary differential equations related to derivatives?

"[ODEs' unknown(s)] involves the derivatives of those functions."

Can partial differential equations have unknowns that are not functions?

"The term 'ordinary' is used in contrast with partial differential equations..."

Can ordinary differential equations have more than one independent variable?

"[ODEs] is dependent on only a single independent variable."

Are ordinary differential equations widely studied in mathematics?

"In mathematics, an ordinary differential equation..."