Kenan kılıçaslan

n-th Order Differential Equation System Solver

This tool numerically solves differential equation systems with 1–5 variables (y, z, u, w, v) and up to 4th-order derivatives using the fixed-step Runge–Kutta–Fehlberg method. You may write the equations using the classical notation y, y', y'', y''', and so on.

Equations

The variables are used in the order y, z, u, w, v. Write the highest derivative in each function as follows:

  • 1st order: y', z', u', w', v'
  • 2nd order: y'', z'', ...
  • 3rd order: y''', z''', ...

Example for a 2nd-order system:
y'' = y' - 2*y + pow(esay, t)
z'' = 2*y - z + exp(-t)

Initial Values

Enter the values of each variable at t = t₀. Depending on the order you selected, use values such as y0, y'0, y''0, y'''0, etc.

Available functions:

pow(x,a), sin(x), cos(x), tan(x), log(x) (ln), exp(x), abs(x), asin(x), acos(x), atan(x), sqrt(x), pi, esay (Euler’s number e), LN2, LN10, Log2e, Log10e.

Use a decimal point (.) for numbers (e.g., 1.0).