Higher-Order Differential Equation Solver

For \(y = y(t)\), this tool solves \(\displaystyle \frac{d^{n}y}{dt^{n}} = f\bigl(t, y, y', y'', \dots\bigr)\) type differential equations of order 1–4 using numerical methods. You may use the following functions and constants:

Function names: pow(t,a), sin(t), cos(t), tan(t), log(t), exp(t), abs(t), asin(t), acos(t), atan(t), sqrt(t)

Constants: pi, esay (the number e), LN2, LN10, Log2e, Log10e

Use a dot as the decimal separator (e.g., 1.25).

For an equation of order \(n\), the user provides only \(\displaystyle y^{(n)} = f(t, y, y', y'', \dots)\). The intermediate derivatives \(y', y'', y'''\) are automatically converted into a system.

Output
\(\displaystyle \frac{d^{2}y}{dt^{2}} = f(t,y,y') =\)

Variable names: t, y, y', y'', y'''. For example, for a second-order equation \(\displaystyle y'' = t\,y' - 2y + e^t\) should be written as t*y'-2*y+pow(esay,t).

Result