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