Inputs
First-order ODEs
ہم Simpson تکملات، integrating factor، عددی inversion، RK4 error، CSV، اور قابلِ اشتراک URLs دکھاتے ہیں۔
Tip: click the canvas to add an initial condition at that point.
Result
How it’s calculated
Teacher notes
FAQ
How is the direction field rendered?
We evaluate the slope on a uniform grid of x and y, clip extreme gradients, and draw short segments so the field stays legible. RK4 runs on the same field to verify the main solution curve.
How do you stabilise the numeric inversion?
For separable equations we scan [y_min, y_max] for a sign change and refine with bisection. Linear equations rely on the integrating factor, and we expose the RK4 discrepancy to monitor the residual error.