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: print maxima("laplace(f(t),t,s)") 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: print maxima("laplace(diff(x(t),t,2),t,s)") ! 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.
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