heaviside and sign function

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Dimitrios Adam
Dimitrios Adam 2020-2-9
评论： Walter Roberson 2020-2-9
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

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Thiago Henrique Gomes Lobato
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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Thiago Henrique Gomes Lobato
Thiago Henrique Gomes Lobato 2020-2-9
编辑：Thiago Henrique Gomes Lobato 2020-2-9
Yes
syms x
Y = 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;
Y2 = subs(Y,sign(x-2),2*heaviside(x-2)-1) % Use subs to replace what you want to
subs(Y,5)
subs(Y2,5)
Y2 =
heaviside(x - 2) + 2*heaviside(x - 2)*exp(2 - x) + (x^2*exp(-x))/2 - x*heaviside(x - 2)*exp(2 - x)
ans =
(25*exp(-5))/2 - 3*exp(-3) + 1
ans =
(25*exp(-5))/2 - 3*exp(-3) + 1

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