Differential Equations & Slope Fields
by Anonymous
Draw slopes on a grid, then add curves that follow them to see what solutions to differential equations look like.
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About this app
Differential Equations and Slope Fields is an interactive calculus learning app that visualizes how a differential equation assigns a slope at each point. Explore slope fields for equations such as y′ = x, y′ = y, y′ = x + y, and y′ = −x/y, then choose starting points to draw solution curves that follow the field. A separate logistic-growth section shows how carrying capacity, growth rate, and starting value affect an S-shaped curve, equilibrium, or decline toward capacity.
Use cases
- High school students learning differential equations and slope fields
- Teachers demonstrating solution curves during calculus lessons
- Learners exploring how initial points change differential-equation solutions
- Students studying logistic growth and carrying capacity
- Math practice sessions focused on visual intuition
Features
- Interactive slope-field visualizations for four differential equations
- Solution curves drawn from selectable starting points
- Three guided tabs: slope field, solution curve, and logistic growth
- Adjustable carrying capacity K, growth rate, and starting value
- Step-by-step missions with reset and next controls