Slope Field Explorer
Generate slope fields for any first-order ODE and trace solution curves through arbitrary initial conditions. Visualize how solutions behave near equilibria, and develop intuition for qualitative analysis.
Exponential Growth & Decay
Model exponential growth and decay processes using differential equations of the form dy/dt = ky. Explore how the solution y = y₀e^(kt) describes phenomena like population growth, radioactive decay, compound interest, and Newton's law of cooling. Understand the significance of the growth constant k, half-life, and doubling time in real-world applications across biology, physics, and finance.
Slope Field Explorer
Slope field generator plotting directional isoclines. Includes an interactive differential Euler-trace mechanism resolving specific math solutions when a distinct Initial Condition point is dropped onto the coordinate grid.
Separable Differential Equations
Slope field visualization with Euler method solution curves for 4 classic separable ODEs (dy/dx=xy, −y/x, y(1−y) logistic, x/y). Adjustable initial condition y₀ with multiple solution curves. Step-by-step separation and integration displayed.