Hi Ayesh,
As per my understanding, you would like to know whether there is any command or function in MATLAB to directly test homogeneity, linearity, and time invariance of differential equations.
In MATLAB, there are no inbuilt commands/functions to test homogeneity, linearity, and time invariance of differential equations. However, you can follow below steps to test the properties in MATLAB.
To Test Homogeneity:
· Generate the input signal.
· Apply differential equations to input and obtain the output.
· Multiply the input signal with constant.
· Apply differential equations to scaled input and obtain the output.
· Compare the original output and scaled outputs to check if they are related by same scaling factor.
To Test Time invariance:
· Generate the input signal.
· Apply differential equations to input and obtain the output.
· Shift the input signal in time.
· Apply differential equations to shifted input and obtain the output.
· Compare the original output and shifted outputs to see if they are related by time shift.
To Test Additive:
· Generate the input signal.
· Apply differential equations to input and obtain the output.
· Add a scalar to the input signal.
· Apply differential equations to new input and obtain the output.
· Compare the original output and new outputs to see if they differ by same scalar factor.
To Test Linearity:
· To test for linearity, check whether the equations satisfy the properties of additive and homogeneity.
I hope this helps!
