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

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