Differential Equations

Study of equations involving derivatives and their applications.

What are Differential Equations?First-Order Differential Equations Initial Value Problems

Advanced Topics

Second-Order Differential Equations Systems of Differential Equations Partial Differential Equations (PDEs)

Practical Applications

Modeling Population Growth Physics: Motion and Forces Medicine: Drug Dosage and Decay

Study Strategies

Break Down the Problem Check Your Solution

What are Differentia...First-Order Differen...Initial Value Proble...Second-Order Differe...Systems of Different...Partial Differential...Modeling Population ...Physics: Motion and ...Medicine: Drug Dosag...Break Down the Probl...Check Your Solution

Advanced Topics

Systems of Differential Equations

Working with Multiple Equations

Sometimes, you need to solve not just one, but several differential equations that are linked together.

Notation

\( \frac{dx}{dt} = ax + by \)
\( \frac{dy}{dt} = cx + dy \)

Why Use Systems?

Many real-life problems involve more than one changing quantity, like predator-prey populations or chemical reactions.

Solving Methods

Substitution and elimination
Matrix methods (for more advanced study)

Examples

Modeling rabbits and foxes in an ecosystem.
Simulating interacting chemicals in a reaction.

In a Nutshell

Systems model situations with multiple interacting variables.

Second-Order Differential Equations

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Partial Differential Equations (PDEs)

Systems of Differential Equations - Differential Equations Content | Practice Hub