Equations

# 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: Runge-Kutta-Fehlberg Show intermediate valuesJust show the result
 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 $$\small\Delta t=$$
 Equation Solution Differential Equations Differential Equation Solution Higher Order Differential Equation Systems of First Order Differential Eq. Systems of nth Order Differential Equations
 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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