# Laplace transform of Mass spring damper differential equation - Issues with input [closed]

de = x''[t] + 6 x'[t] + 8 x[t] == 10
80 + 6 Derivative[x][t] + (x^\[Prime]\[Prime])[t] == 10

Initial = {x -> 0, x' -> 0}

Lde = LaplaceTransform[de, t, s]
80/s - Derivative[x] == 10/s

Lde = Lde /. Initial
80/s == 10/s

Solve[Lde, LaplaceTransform[x[t], t, s]]
Solve::ivar: 10/s is not a valid variable.


Hello, using the trail version of mathmatica I have a Differetial equation (de) and want to find the laplace transform of it and model X[t] and x[s]. Ive used various resources to get to this point but cannot get past the last line.

It states that 10/s is not a valid variable - but this is my input???

Any help would be appreciated!

## closed as off-topic by zhk, bbgodfrey, ubpdqn, MarcoB, EdmundMar 21 '17 at 0:09

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• Do you have some existing definitions that are causing problems? Perhaps try again with a fresh kernel (via the menu "Evaluation > Quit Kernel") – mikado Mar 18 '17 at 18:26
• 8 x[t] is replaced by 80 in the first line, suggesting that x[t] has already been defined as 10 in code preceding that in the question. This issue probably invalidates everything that follows. – bbgodfrey Mar 19 '17 at 4:13

lt = LaplaceTransform[de, t, s] /. Initial;
sol = Solve[lt, LaplaceTransform[x[t], t, s]];
InverseLaplaceTransform[sol[[1, 1, 2]], s, t] DSolve[{x''[t] + 6 x'[t] + 8 x[t] == 10, x == 0, x' == 0}, x[t], t] Plot[x[t] /. %, {t, 0, 30}, PlotRange -> All]

• Thanks very much for that Maple and after starting a new kernel - (cheers mikado) it worked. Going to construct it so I can understand the response of MSD systems better. – Benjamin Crump Mar 18 '17 at 21:00