sage: _ = maxima.eval("f(t) := t*sin(t)") sage: maxima("laplace(f(t),t,s)") 2*s/(s^2 + 1)^2
sage: maxima("laplace(delta(t-3),t,s)") #Dirac delta function %e^-(3*s)
sage: _ = maxima.eval("f(t) := exp(t)*sin(t)") sage: maxima("laplace(f(t),t,s)") 1/(s^2 - 2*s + 2)
sage: _ = maxima.eval("f(t) := t^5*exp(t)*sin(t)") sage: maxima("laplace(f(t),t,s)") 360*(2*s - 2)/(s^2 - 2*s + 2)^4 - 480*(2*s - 2)^3/(s^2 - 2*s + 2)^5 + 120*(2*s - 2)^5/(s^2 - 2*s + 2)^6 sage: maxima("laplace(f(t),t,s)").display2d() 3 5 360 (2 s - 2) 480 (2 s - 2) 120 (2 s - 2) --------------- - --------------- + --------------- 2 4 2 5 2 6 (s - 2 s + 2) (s - 2 s + 2) (s - 2 s + 2)
sage: maxima("laplace(diff(x(t),t),t,s)") s*laplace(x(t),t,s) - x(0)
sage: maxima("laplace(diff(x(t),t,2),t,s)") -at('diff(x(t),t,1),t = 0) + s^2*laplace(x(t),t,s) - x(0)*s
It is difficult to read some of these without the 2d representation:
sage: maxima("laplace(diff(x(t),t,2),t,s)").display2d() ! d ! 2 - -- (x(t))! + s laplace(x(t), t, s) - x(0) s dt ! !t = 0
Even better, use view(maxima("laplace(diff(x(t),t,2),t,s)"))
to see
a typeset version.
See About this document... for information on suggesting changes.