MATLAB: Heaviside and sign function

differential equationsheaviside

Hello,
i have for example this differential equation
ode = diff(y,x,2)+2*diff(y,x,1)+y==exp(-x)+heaviside(x-2)-dirac(x-2);
cond1 = y(0) == 0;
cond2 = Dy(0) == 0;
Τhe problem is when i solve it the result contains the fucntion sign instead of heaviside:
ySol(x) =
sign(x – 2)/2 + (x^2*exp(-x))/2 + exp(2 – x)*(sign(x – 2) + 1) – x*exp(2 – x)*(sign(x – 2)/2 + 1/2) + 1/2
Do you know how can i change the sign in the result and only have heaviside function?
Thank you

Best Answer

The heavside function is not the same as the sign function, you can't simply change one for another. If you want to write the sign function in terms of a heavside function you can use the following relation:
Where is the heavside function.
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