High Order Differential Equation Solver

The differential equation you want to solve:
Order

Formula:

Variable symbols
$\displaystyle {\frac{d^2y}{dt^2}}=f(t,y,y')=$
Necessary boundary conditions for solution:
$\displaystyle t_{0}=$
$\displaystyle y_{0}=$
$\displaystyle y'_{0}=$
The desired $t$ value to be found:
$t_n=$
Increment $\Delta t=$
Functions to be used in the equation:

$\begin{array}{lllll} x^a & : & \mathrm{pow(x,a)} \\sin\, x & : & \mathrm{sin(x)} &cos\,x & : & \mathrm{cos(x)} \\tan\,x & : & \mathrm{tan(x)} & ln\,x & : &\mathrm{log(x)} \\e^x & : & \mathrm{exp(x)} &\left|x\right| & : & \mathrm{abs(x)} \\arcsin\,x & : & \mathrm{asin(x)} &arccos\,x& : & \mathrm{acos(x)} \\arctan\,x & : & \mathrm{atan(x)} &\sqrt{x} & : & \mathrm{sqrt(x)} \\\pi & : &\mathrm{pi} &e \mathrm{ number} & : & \mathrm{esay} \\ln\,2 & : &\mathrm{LN2} & ln\,10 & : & \mathrm{LN10} \\log_{2}\,e & : & \mathrm{Log2e} &log_{10}\,e & : & \mathrm{Log10e} \end{array}$

y' (single comma quotation mark) for first derivate,
y'' (two single comma quotation mark) for second derivate,
y''' (three single comma quotation mark) for third derivate

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