MATLAB: Inverse laplace of s certain function

inverse laplace

hello. I am trying to find the inverse laplace of a function such as exp(-3s)^2/(s-4) which I know the answer will have a unit step which is the Heaviside but unfortunately it is outputting me the same what I typed;ilaplace(f).Any ideas how to get the answer?

Best Answer

It works for me in R2017b:

syms s t 
F = exp(-3*s)^2/(s-4);
f = ilaplace(F,s,t)
f =
heaviside(t - 6)*exp(4*t - 24)

Related Solutions

MATLAB: R2009a matlab code for laplace and inverse laplace

You need the Symbolic Math Toolbox™

Examples on how to use the laplace function:

syms t
f = t^4
laplace(f)
syms s
g = 1/sqrt(s)
laplace(g)
syms t a x
f = exp(-a*t)
laplace(f,x)

Examples on how to use ilaplace

syms s
f = 1/s^2
ilaplace(f)
syms a t
g = 1/(t-a)^2
ilaplace(g)
syms x u
syms a real
f = 1/(u^2-a^2)
simplify(ilaplace(f,x))

MATLAB: How to put the step function into the differential equation solution, h.. in this case

I do not understand what you are trying to do. The approach I would take would be

syms y(t) s
eqn = diff(y(t), t, t)+4*y(t) == 4*t*(heaviside(t)-heaviside(t-1))+4*heaviside(t-1)
ode = dsolve(eqn, y(0)==1, subs(diff(y(t),t),t,0)==0)
laplace(ode, t, s)

I would not attempt a laplace before doing the dsolve because at that point the equation has not been sufficiently resolved to do a laplace. The h part has a nice laplace transform but the other side does not.

But if you must...

    syms y(t) s Y
    eqn = diff(y(t), t, t)+4*y(t) == 4*t*(heaviside(t)-heaviside(t-1))+4*heaviside(t-1)
    sol = ilaplace( solve( subs(laplace(eqn, t, s), laplace(y(t), t, s), Y), Y), s, t)
    yt = subs(sol, {y(0), sym('D(y)(0)')}, {1, 0})

Best Answer

Related Solutions

MATLAB: R2009a matlab code for laplace and inverse laplace

MATLAB: How to put the step function into the differential equation solution, h.. in this case

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