Calculations

# Higher Order Differential Equation Solution

The solution of high order differential equations in the form of $\displaystyle {\frac{d^{n}y}{dt^{n}}}=f(t,y^{(n-1)},y^{(n-2)}, \dots, y',y)$ is made by numerical analysis method. Use the variables $t$, $y'''$, $y''$, $y'$ and $y$. 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). (Currently, up to the 4th order is calculated.)

 The differential equation you want to solve: Order Formula: Runge-Kutta-Fehlberg Runge-Kutta Adams-Moulton Metodu
 Variables $\displaystyle {\frac{d^2y}{dt^2}}=f(t,y,y')=$ Necessary boundary conditions for solution: $\displaystyle t_{0}=$ $\displaystyle y_{0}=$ $\displaystyle y'_{0}=$ The desired $t$ value $t_n=$ Increment $\Delta t=$
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 Functions to be used in equations:$\begin{array}{lll|lll} t^a & : & \mathrm{pow(t,a)} \\\sin\, t & : & \mathrm{sin(t)} &\cos\,t & : & \mathrm{cos(t)} \\\tan\,t & : &\mathrm{tan(t)} &\ln\,t & : & \mathrm{log(t)} \\e^t & : & \mathrm{exp(t)} &\left|t\right| & : & \mathrm{abs(t)} \\\arcsin\,t & : & \mathrm{asin(t)} &\arccos\,t & : & \mathrm{acos(t)} \\\arctan\,t & : & \mathrm{atan(t)} &\sqrt{t} & : & \mathrm{sqrt(t)} \\ \\\pi & : & \mathrm{pi} &e \mathrm{ sayısı} & : & \mathrm{esay} \\\ln\,2 & : &\mathrm{LN2} & \ln\,10 & : & \mathrm{LN10} \\\log_{2}\,e & : & \mathrm{Log2e} & \log_{10}\,e & : & \mathrm{Log10e} \end{array}$y' for first derivative (one single quotation mark),y'' for second derivative (two single quotation marks), y''' for third derivative (three single quotation marks) will be written.

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