# Solve Partial Differential Equation

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soe on 17 Jan 2018
Answered: SAI SRUJAN on 27 Mar 2024
Let D=(d/dx+fn d/dy) fn=f(xn,yn) Then, Df=(d/dx+fn d/dy)f=fx+ffy D2f=(d/dx+fd/dy)^2 f(xn,yn) =(d/dx+f d/dy) (fx + ffy) Then, how can I find D4f using MATLAB?

SAI SRUJAN on 27 Mar 2024
Hi soe,
I understand that you are trying to solve a partial differential equation.
To find 'D4f' using MATLAB, you can use the Symbolic Math Toolbox. Please go through the following code snippet to proceed further,
syms x y f
fn = f(x, y);
D = diff(f, x) + fn * diff(f, y);
D2 = diff(D, x) + fn * diff(D, y);
D3 = diff(D2, x) + fn * diff(D2, y);
D4 = diff(D3, x) + fn * diff(D3, y);
In this code, we define the symbolic variables 'x', 'y', and 'f'. Then, we define 'fn' as a function of 'x' and 'y'. We calculate 'D'and we continue this process to calculate 'D2', 'D3', and finally 'D4', which represents the fourth derivative of 'f' with respect to 'x' and 'y'.
For a comprehensive understanding of the 'diff' function in MATLAB, please refer to the following documentation.
I hope this helps!