### Related

##### laplace-unit_step

laplace (5 * unit_ste...

Calculate

laplace (1,t,s);

Calculate

##### laplace

laplace((t),s,t);

laplace((2),s,t);

Calculate

##### laplace

inv_laplace(s^2+5s+6)...

Calculate

##### laplace

invers_laplace (1/((s...

Calculate

f:t^2;

laplace(f,t,s);

Calculate

##### laplace-ratsimp-sin

laplace(t*%e^(3*t)*si...

ratsimp(%);

Calculate

##### laplace

f(t) := 8*t^2 *(unit_...

laplace(f(t),t,z);

laplace(8*t^2*(unit_s...

Calculate

##### laplace

inv_laplace(2/(s^2+s)...

Calculate

laplace(t,t,s);

laplace(1,t,s);

Calculate

### laplace

Run Example
```(%i1)assume(V>
0, R>
0, L>
0, C>
0);
(%o1)                    [V > 0, R > 0, L > 0, C > 0]
(%i2) assume(C*R^2 - 4*L >
0);
2
(%o2)                            [C R  > 4 L]
(%i3) ec  : R*x(t) + L*diff(x(t),t) + integrate(x(t), t)/C = V;
/
[
I x(t) dt
]
d              /
(%o3)               x(t) R + (-- (x(t))) L + --------- = V
dt                 C
(%i4) ecd : diff(ec, t);
2
d               d               x(t)
(%o4)              (-- (x(t))) R + (--- (x(t))) L + ---- = 0
dt                2              C
dt
(%i5) e2:laplace(ecd,t,s);
!
d        !
(%o5) (s laplace(x(t), t, s) - x(0)) R + (- -- (x(t))!
dt       !
!t = 0
2                                   laplace(x(t), t, s)
+ s  laplace(x(t), t, s) - x(0) s) L + ------------------- = 0
C
(%i6) atvalue( x(t), t=0, 0);
(%o6)                                  0
(%i7) atvalue( diff(x(t), t), t=0, V/L);
V
(%o7)                                  -
L
(%i8) e4:solve(e2,laplace(x(t),t,s));
!
d        !
x(0) C R + (-- (x(t))!      + x(0) s) C L
dt       !
!t = 0
(%o8)  [laplace(x(t), t, s) = -----------------------------------------]
2
s C R + s  C L + 1
(%i9) ilt(e2,s,t);
(%o9) ilt((s laplace(x(t), t, s) - x(0)) R, s, t)
!
d        !         2
+ ilt((- -- (x(t))!      + s  laplace(x(t), t, s) - x(0) s) L, s, t)
dt       !
!t = 0
laplace(x(t), t, s)
+ ilt(-------------------, s, t) = 0
C
(%i10) ```
Run Example
```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) ```

Help for Laplace