heaviside and sign function
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Dimitrios Adam
il 9 Feb 2020
Commentato: Walter Roberson
il 9 Feb 2020
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
Risposta accettata
Thiago Henrique Gomes Lobato
il 9 Feb 2020
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:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/270674/image.png)
Where
is the heavside function.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/270675/image.png)
3 Commenti
Thiago Henrique Gomes Lobato
il 9 Feb 2020
Modificato: Thiago Henrique Gomes Lobato
il 9 Feb 2020
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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