First-Order ODE Solver

Summary

Enter your ODE as dy/dx = f(x,y), set initial conditions and step size, then get a step-by-step Euler method table and solution curve.

How it works

1. Enter the right-hand side expression f(x,y) for your ODE dy/dx = f(x,y).
2. Set the initial condition: the starting x value (x0) and corresponding y value (y0).
3. Choose a step size h and the total number of steps to compute.
4. Click "Solve" to run Euler's method: yn+1 = yn + h * f(xn, yn).
5. Review the step-by-step table showing x, y, f(x,y), and the slope at each step.
6. Inspect the solution curve chart to visualize how y evolves over x.

Use cases

• Check homework solutions for introductory differential equations courses.
• Visualize approximate solutions before applying exact analytical methods.
• Explore how step size affects Euler method accuracy.
• Model simple population growth or decay described by dy/dx = ky.
• Analyze velocity under variable forces in physics problems.
• Prototype numerical integration logic before coding it in Python or MATLAB.
• Teach or learn numerical methods interactively.
• Quickly estimate trajectories in engineering dynamics problems.

Frequently Asked Questions