Introduction to Differential Equations 🧠

Interactive Tutorial • Practice Problems • Speed Quiz

What are Differential Equations? 🤔

A **differential equation** (or "DE") is an equation that involves an unknown function and one or more of its derivatives. Think of it as a rule that describes how a quantity changes based on its current value.

The main goal when solving a DE is to find the original function that satisfies the equation. For example, if you have the equation $\frac{dy}{dx} = 2x$, you need to find a function $y$ whose derivative is $2x$. The solution is $y = x^2 + C$. The "C" is a **constant of integration**, making the solution a **family of functions**.

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Video: Visualizing Solutions 🎬

Watch how different initial conditions change the specific solution to a differential equation.

Practice Problems (Solving Separable DEs)

Solve the following first-order differential equations by separating the variables.

1) $\frac{dy}{dx} = 3x^2$
2) $\frac{dy}{dx} = 2y$
3) $\frac{dy}{dx} = \frac{x}{y}$
4) $\frac{dy}{dx} = \cos(x)$

⚡ Differential Equations Speed Quiz

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