MATLAB: Laplace transform of integral

integrallaplace

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

Best Answer

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)
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