heaviside and sign function

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

[Walter Roberson]

rewrite(ySol, 'Heaviside')

Possibly

Answer 1

[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.

[Dimitrios Adam]

Thank you,

but if i want to show the result with only the heaviside and not the sign can i somehow format the result ?

[Thiago Henrique Gomes Lobato]

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

[Dimitrios Adam]

Thank you very much !!