Differential Equations Lab

System

Parameters

P1 (b): 0.50P2 (k): 10.00

Initial Conditions

x0: 1.0v0: 0.0dt: 0.01

System Info

Discriminant: b²-4mk = -39.75

Type: Underdamped

ω0 = 3.16 rad/s

Differential Equations Solver – ODE Visualizer

Differential equations describe how quantities change in relation to one another, governing everything from population growth to electrical circuits to heat transfer. This solver lets you enter a first-order or second-order ODE, generate the slope field that encodes all possible solution behaviors, and plot particular solutions for any initial condition you choose. Numerical methods like Euler's and Runge-Kutta run alongside the exact analytical solution so you can see where approximation error accumulates.

What you can do in this simulation

Enter a first-order ODE and generate its slope field across a configurable domain
Click any point on the slope field to trace the solution curve through that initial condition
Apply Euler's method with an adjustable step size and compare the numerical vs exact solution
Solve classic models: exponential growth, logistic population, and simple harmonic oscillator
Switch to a phase-plane view for second-order systems and observe equilibrium stability

Concepts covered

differential equations · slope field · initial value problem · Euler's method · Runge-Kutta · phase plane

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