Understanding Differential Equations in Algebra

Differential equations involve equations with derivatives. They are used to model real-world phenomena in science and engineering.

What is a Differential Equation?

A differential equation contains derivatives of an unknown function.

Types of Differential Equations

• Ordinary Differential Equations (ODEs)
• Partial Differential Equations (PDEs)

Solving Differential Equations

Methods include separation of variables, integrating factors, and characteristic equations.

Practice Problems

1. Solve \( \frac{dy}{dx} = 3x^2 \).
2. Solve \( \frac{dy}{dx} + y = 0 \).
3. Classify: \( \frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2} \).