# Homogen Differential Equations Solving (update:27-06-07)

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homogen differential equation generally solution technique
Updated 27 Jun 2007

[Description:]
In this application is descriptioned homogen-differential equations generally solutions with matlab symbolic tool's.

Generally homogen-differential equation's form is (where R=[d/dx] ) sum {i=1:n} [C_(i)*R^{i}].y=0

Here, firstly sub function-[regsolution.m] solving differential equation's polynomial form and determine all roots order-degree, secondly it is sub function-[homsolution.m] analysis all roots be complex or real value's with order-degree and outputs differential equations generally solution of regular format. This [homsolution.m] sub-mosule's (func) be possible matrix format.

I wish, this work will be usefuly of several mathematical areas.

[Example:]
homsolution(R^4+R^3+2*R^2-R+3) <---|
%
%R^4+R^3+2*R^2-R+3
%
%+exp^(-1+1.4142ix).(C4)+exp^(-1-1.4142ix).(C3)+exp^(0.5+0.86603ix).(C2)+exp^(0.5-0.86603ix).(C1)
% 0.5000 - 0.8660i 1.0000
% 0.5000 + 0.8660i 1.0000
% -1.0000 - 1.4142i 1.0000
% -1.0000 + 1.4142i 1.0000

### Cite As

Ali OZGUL (2024). Homogen Differential Equations Solving (update:27-06-07) (https://www.mathworks.com/matlabcentral/fileexchange/15439-homogen-differential-equations-solving-update-27-06-07), MATLAB Central File Exchange. Retrieved .

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