Differential Equations Solver
The two starter equations, solved exactly: growth and decay (dy/dx = k·y) and approach-to-balance (dy/dx = a·y + b), with an initial value.
Example — dy/dx = 0.1y, y(0) = 100, find y(10)y(10) = 271.83
How we got it — the example, step by step
- dy/dx = k·y is the growth/decay equation. Its solution is an exponential: y = y0 × e^(k(x − x0)).
- Put the numbers in: y = 100 × e^(0.1 × 10) = 100 × e^1.
- e ≈ 2.71828, so y ≈ 271.83.
Check it backwards
Differentiate the solution and you get 0.1 × y — the equation we started with. And at x = 0 it gives 100, the starting value.
Questions people also ask
Which differential equations can it solve?
Two families, exactly: dy/dx = k·y (growth and decay) and dy/dx = a·y + b (growth toward or away from a balance point), each with a starting value. Other forms are not in yet, and this page says so rather than printing a wrong 'solution'.