Laplace transform of integral

I am trying to take the Laplace transform of the following equation using 2019a:

I am having an issue with the integral, which I know should come out to be y(s)/s.

I have tried

I = laplace(int('y(x)','x','0','t'),t,s)y(x) ,    x’,’0’,’t’),t,s) 

and more basically:

syms y(x) s t x

R = int(y,t,0,t)
laplace(R)

but I keep getting y(s)/s^2

Any help is much appreciated in advance

Answer 1

[Walter Roberson]

syms y(x) s t x
R = int(y,t,0,t)

y is a function of x, which is independent of t, so y(x) is constant as far as integrating with respect to t is concerned.

syms y(u) s t L
assume(s ~= 0);
Dy = diff(y,u)
eqn = Dy(t) + y(t) + int(y,u,0,t) == cos(t)
I = laplace(eqn,t,s)
Is = simplify(I, 'steps',10);
Lt = laplace(y(t),t,s);
ylap = Lt == solve(subs(Is, Lt, L),L)

[Erik Conrath]

Thank you! Question, shouldnt the output of taking the Laplace of the integral function be L*(1/s) not just simply L? Or did Matlab switch the physical position of the Laplace transform of y(t) and the Laplace transform of the integral in I?

[Erik Conrath]

I see it now after extracting just the integral..thanks again.

[Daniel Martinez]

How can initial values be added in the code?