### Related

##### ilt

eq:625/((6.4e-05*s^5)...

ilt(eq,s,t);

Calculate

##### ilt-plot2d

f(t):=ilt(1000*(s^2+s...

f(t);

plot2d(f(t),[t,0,0.1]);

Calculate

##### ilt-laplace-plot2d

conv(f1, f2, x) := il...

fN(x,a) := if x>=-...

fS(x) := if x=-1 or x...

Calculate

##### ilt

i1(s):= (12*s + 12000...

i1(t):= ilt(i1(s),s,t);

Calculate

##### ilt

ilt(1/(1/s^4 + 6.086*...

Calculate

##### ilt

F(s):=(2*s+1)/(s^2+4)^2;

ilt(F(s),s,t);

Calculate

##### ilt

W: (4*s/(2*s^3+42.05*...

stepresp: ilt(W*(1/s)...

impulseresp: ilt(W,s,t);

Calculate

##### ilt-partfrac

ilt( 4*(s)/(s^2+2*s+5...

partfrac(4*(s)/(s^2+2...

Calculate

ilt(F,s,t);

Calculate

ilt(1,p,x);

Calculate

### ilt

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
```f=ilt(s/((s^2+1)*((s-1)^2+1)),s,t);
2 sin(t)     t  3 sin(t)   cos(t)    cos(t)
(%o1)          f = - -------- + %e  (-------- - ------) + ------
5               5         5         5
(%i2) g=ilt((s-2)/(s^2-2*s+2),s,t);
t
(%o2)                      g = %e  (cos(t) - sin(t))
(%i3) simplify(f+g);
(%o3)                           simplify(g + f)
(%i4) ```
Run Example
```laplace(R*(1-exp(-t/T)),t,s);
1     1
(%o1)                            R (- - -----)
s   1
- + s
T
(%i2) ilt(s * R * (1/s-1/(1/T+s)),s,t);
- t/T
R %e
(%o2)                              ---------
T
(%i3) laplace(sin(w*t)*sin(w*t+phi),t,s);
2
2 cos(phi) w  + sin(phi) s w
(%o3)                    ----------------------------
2    3
4 s w  + s
(%i4) ```

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