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laplace-plot2d-unit_step
plot2d(f(t),[t,0,5],[y,-5,5]);

f(t):= unit_step(t)*t...

plot2d(f(t),[t,0,5],[...

laplace(f(t),t,s);

Calculate

laplace

inv_laplace(e^(s)/s,t...

Calculate

laplace-plot2d-unit_step
plot2d(f(t),[t,0,5],[y,0,10]);

f(t):= t^2*unit_step(...

plot2d(f(t),[t,0,5],[...

laplace(f(t),t,s);

Calculate

laplace-plot2d-unit_step
plot2d(f(t),[t,0,5],[y,-5,5]);

f(t):= unit_step(t) -...

plot2d(f(t),[t,0,5],[...

laplace(f(t),t,s);

Calculate

laplace-unit_step

u0(t) := unit_step;

f(t) := t*u0(t);

laplace(f(t),t,s);

Calculate

laplace-sin

laplace(sin(4*t),t,s);

Calculate

laplace

inv_laplace((A*e^(-3....

Calculate

laplace

laplace (1/2*t*t,t,s);

Calculate

laplace

ilaplace (1/s);

Calculate

laplace-unit_step

g= laplace(unit_step(...

Calculate

laplace

Run Example
(%i1)defint(x,x,a-b,a);
                              2    2            2
                             a    b  - 2 a b + a
(%o1)                        -- - ---------------
                             2           2
(%i2) eq1:sin(w*x);
(%o2)                              sin(w x)
(%i3) eq2:defint(eq1,x,a-b,a);
                           cos((a - b) w)   cos(a w)
(%o3)                      -------------- - --------
                                 w             w
(%i4) laplace(eq2,a,s);
                     w sin(b w) + s cos(b w)        s
(%o4)                ----------------------- - -----------
                               2    2              2    2
                           w (w  + s )         w (w  + s )
(%i5) 
Run Example
Gc:0;
(%o1)                                  0
(%i2)  Rg:0;
(%o2)                                  0
(%i3)  Ro1:0;
(%o3)                                  0
(%i4)  Ro2:0;
(%o4)                                  0
(%i5) v(t):=0;
(%o5)                              v(t) := 0
(%i6) i(t):=IL;
(%o6)                             i(t) := IL
(%i7) atvalue(vc(t), t=0, VG);
(%o7)                                 VG
(%i8) atvalue(ig(t), t=0, IL);
(%o8)                                 IL
(%i9) atvalue(i1(t), t=0, IL);
(%o9)                                 IL
(%i10) atvalue(i2(t), t=0, 0);
(%o10)                                 0
(%i11) atvalue(vut1(t), t=0, 0);
(%o11)                                 0
(%i12) atvalue(iut1(t), t=0, 0);
(%o12)                                 0
(%i13) vFW1(t):=-VG;
(%o13)                          vFW1(t) := - VG
(%i14) iFW1(t):=0;
(%o14)                           iFW1(t) := 0
(%i15) vFW2(t):=0;
(%o15)                           vFW2(t) := 0
(%i16) atvalue(vut2(t), t=0, 0);
(%o16)                                 0
(%i17) eqi1:laplace(ig(t) = Gc*vc(t) + C*'diff(vc(t),t,1) + i(t),t,s);
                                                                   IL
(%o17)    laplace(ig(t), t, s) = C (s laplace(vc(t), t, s) - VG) + --
                                                                   s
(%i18) eqi2:laplace(i(t) + iFW1(t) = i1(t),t,s);
                           IL
(%o18)                     -- = laplace(i1(t), t, s)
                           s
(%i19) eqi3:laplace(Gc*vc(t) + C*'diff(vc(t),t,1) + iut1(t) = iFW1(t),t,s);
(%o19)   C (s laplace(vc(t), t, s) - VG) + laplace(iut1(t), t, s) = 0
(%i20) eqv1:laplace(VG = Rg*ig(t) + v(t) + Ro1*i1(t) + Lo1*'diff(i1(t),t,1) + Lu*'diff(i2(t),t,1),t,s);
       VG
(%o20) -- = Lo1 (s laplace(i1(t), t, s) - IL) + Lu s laplace(i2(t), t, s)
       s
(%i21) eqv2:laplace(vut1(t) = vFW1(t) + Ro1*i1(t) + Lo1*'diff(i1(t),t,1) + Lu*'diff(i2(t),t,1),t,s);
                                  VG
(%o21) laplace(vut1(t), t, s) = - -- + Lo1 (s laplace(i1(t), t, s) - IL)
                                  s
                                                    + Lu s laplace(i2(t), t, s)
(%i22) eqv3:laplace(v(t) = vc(t) + vFW1(t),t,s);
                                                    VG
(%o22)                   0 = laplace(vc(t), t, s) - --
                                                    s
(%i23) eqv4:laplace(vut2(t) = vFW2(t) + Ro2*i2(t) + Lo2*'diff(i2(t),t,1) + Lu*'diff(i1(t),t,1),t,s);
(%o23) laplace(vut2(t), t, s) = Lu (s laplace(i1(t), t, s) - IL)
                                                   + Lo2 s laplace(i2(t), t, s)
(%i24) sol:solve([	eqi1,	eqi2,	eqi3,	eqv1,	eqv2,	eqv3,	eqv4],[	'laplace(vc(t),t,s),	'laplace(ig(t),t,s),	'laplace(i1(t),t,s),	'laplace(iFW1(t),t,s),	'laplace(i2(t),t,s),	'laplace(vut2(t),t,s),	'laplace(vFW1(t),t,s)]);
(%o24)                                []
(%i25) 
Run Example
laplace(t*unit_step(t-4)-unit_step(t-6),t,s);
                             - 4 s     - 4 s     - 6 s
                         4 %e        %e        %e
(%o1)                    --------- + ------- - -------
                             s          2         s
                                       s
(%i2) 

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