📈 Slope Field Plotter

🎯 Getting Started

This tool generates a slope field (direction field) for first-order differential equations of the form dy/dx = f(x, y). Visualizing the "flow" helps you understand the general solution before calculating specific ones.

• Slope Field: Grid of small arrows showing the slope at each point
• Initial Value Problems: Click anywhere on the graph to draw a solution curve through that point
• Multiple Solutions: Add multiple solution curves to see the family of solutions

✏️ Equation Input

Enter the right-hand side of dy/dx = f(x,y):

• Variables: Use x and y
• Basic Operations: +, -, *, /, ^ (power)
• Functions: sin(x), cos(y), exp(x), ln(y), sqrt(x+y)
• Constants: Use numbers like 2, 3.14, or pi, e

🖱️ Interactive Features

• Click to Plot: Click anywhere on the slope field to draw a solution curve through that point
• Clear Solutions: Use the "Clear Solutions" button to remove all solution curves
• Adjust View: Change the x and y ranges to zoom in/out
• Arrow Density: Modify the grid size to add more or fewer arrows

🔢 Quick Start Examples

Expand the "Quick Examples" section below to instantly load pre-configured equations with optimal view settings. Just click any example card!