# 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[1][x][t] + (x^\[Prime]\[Prime])[t] == 10

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

Lde = LaplaceTransform[de, t, s]
80/s - Derivative[1][x][0] == 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!

• 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;

DSolve[{x''[t] + 6 x'[t] + 8 x[t] == 10, x[0] == 0, x'[0] == 0}, x[t], t]

Plot[x[t] /. %, {t, 0, 30}, PlotRange -> All]