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Systems of nth Order Differential Equations

Differential equation systems in the form of \(\displaystyle \small {\frac{d^ny}{dt^n}}=f_1(t,y,z,\cdots,y^{(n)},z^{(n)})\), \(\displaystyle \small {\frac{d^nz}{dt^n}}=f_2(t,y,z,\cdots,y^{(n)},z^{(n)})\) are solved by numerical analysis method. (For now, solutions up to 4th order and 5 equations are made.) You can use the +, -, *, / math operators and the following functions. Use the pow function to take the exponent. For example, for \(t^ 2\), type pow (t, 2).

The differential equation you want to solve:
Equation number
Order
Formula:

Variable symbols
\(y''=f(t,y,y',z,z')\)
\(z''=f(t,y,y',z,z')\)
Necessary boundary conditions for solution
\(\displaystyle\small t_{0}=\)
\(\displaystyle\small y_{0}=\)
\(\displaystyle\small y'_{0}=\)
\(\displaystyle\small z_{0}=\)
\(\displaystyle\small z'_{0}=\)
The desired \(t\) value
\(\small t_n=\)
Increment \(\small\Delta t=\)

Functions to be used in equations:
\(\begin{array}{lll|lll} x^a & : & \mathrm{pow(x,a)} \\\sin\, x & : & \mathrm{sin(x)} &\cos\,x & : & \mathrm{cos(x)} \\\tan\,x & : &\mathrm{tan(x)} &\ln\,x & : & \mathrm{log(x)} \\e^x & : & \mathrm{exp(x)} &\left|x\right| & : & \mathrm{abs(x)} \\\arcsin\,x & : & \mathrm{asin(x)} &\arccos\,x & : & \mathrm{acos(x)} \\\arctan\,x & : & \mathrm{atan(x)} &\sqrt{x} & : & \mathrm{sqrt(x)} \\ \\\pi & : & \mathrm{pi} &e \mathrm{ sayısı} & : & \mathrm{esay} \\\ln\,2 & : &\mathrm{LN2} & \ln\,10 & : & \mathrm{LN10} \\\log_{2}\,e & : & \mathrm{Log2e} & \log_{10}\,e & : & \mathrm{Log10e} \end{array}\)

\(y'\), \(z'\),\(u'\),\(w'\) for first derivative (one single quotation mark),
\(y''\), \(z''\),\(u''\),\(w''\) for second derivative (two single quotation marks),
\(y'''\), \(z'''\), \(u'''\), \(w'''\) for third derivative (three single quotation marks) will be written.
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