11
syms t
>> laplace (exp(t+7))
ans = exp(7)/(s-1)
12
>> syms t
>> laplace (exp((-2*t)-5))
ans = exp(-5)/(s+2)
13
>> syms t
>> laplace (t*(exp(4*t)))
ans = 1/(s-4)^2
14
syms t
>> laplace ((t^2)*(exp(3*t)))
ans = 2/(s-3)^3
15
laplace ((exp(t))*(sin(t)))
ans = 1/((s-1)^2+1)
16
syms t
>> laplace ((exp(t))*(cos(t)))
ans = (s-1)/((s-1)^2+1)
17
>> syms t
>> laplace ((t)*(cos(t)))
ans = 1/(s^2+1)*cos(2*atan(1/s))
18
>> syms t
>> laplace ((t)*(sin(t)))
ans = 1/(s^2+1)*sin(2*atan(1/s))
19
>> syms t
>> laplace (2*(t^4))
ans = 48/s^5
20
>> syms t
>> laplace (t^5)
ans =120/s^6
21
>> syms t
>> laplace ((4*t)-10 )
ans = 4/s^2-10/s
22
>> syms t
>> laplace ((4*t)+3)
ans = 4/s^2+3/s
23
>> syms t
>> laplace ((t^2)+(6*t)-3)
ans = 2/s^3+6/s^2-3/s
24
>> syms t
>> laplace ((-4*(t^2))+(16*t)+9)
ans = -8/s^3+16/s^2+9/s
25
>> syms t
>> laplace ((t+1)^3)
ans = 6/s^4*exp(s)*exp(-s)*(1+s+1/2*s^2+1/6*s^3)
26
>> syms t
>> laplace (((2*t)-1)^3)
ans = 48/s^4-24/s^3+6/s^2-1/s
27
>> syms t
>> laplace (1+(exp(4*t)))
ans = 1/s+1/(s-4)
28
>> syms t
>> laplace ((t^2)-(exp(9*t))+5)
ans = 2/s^3-1/(s-9)+5/s
29
>> syms t
>> laplace (1+(exp(2*t)))^2
ans = (1/s+1/(s-2))^2
30
>> syms t
>> laplace ((exp(t))-(exp(-t)))^2
ans =(1/(s-1)-1/(1+s))^2
31
>> syms t
>> laplace ((4*(t^2))-(5*(sin(3*t))))
ans = 8/s^3-15/(s^2+9)
32
>> syms t
>> laplace ((cos(5*t))+(sin(2*t)))
ans = 1920*s/(s^2+1)/(s^2+9)/(s^2+25)*(7/6+1/6*s^2+1/120*(s^2+1)*(s^2+9))-120*s/(s^2+1)/(s^2+9)*(7/6+1/6*s^2)+5*s/(s^2+1)+2/(s^2+4)
>>
La transformada inversa de laplace.
1
('F(t)=(1/s^3), s, t);
(F(t),s,t) = t^2/2
2
('F(t)=(1/s^4), s, t);
(F(t),s,t) = t^3/6
3
('F(t)=((1/s^2)-(48/s^5)), s, t);
(F(t),s,t) = t-2*t^4
4
>> syms s
>> ilaplace ((2/s)-(1/(s^3)))^2
ans = 1/120*t^5-2/3*t^3+4*t
5
>> syms s
>> ilaplace (((s+1)^3)/(s^4))
ans = 1/6*t^3+3/2*t^2+3*t+1
6
>> syms s
>> ilaplace (((s+2)^2)/(s^3))
ans = 2*t^2+4*t+1
7
>> syms s
>> ilaplace (1/(s^2))-(1/(s))+(1/(s-2))
ans = t-1+exp(2*t)
8
>> syms s
>> ilaplace (4/(s))+(6/(s^5))-(1/(s+8))
ans = 4+1/4*t^4-exp(-8*t)
9
>> syms s
>> ilaplace (1/((4*s)+1))
ans = 1/4*exp(-1/4*t)
10
>> syms s
>> ilaplace (1/((5*s)-2))
ans = 1/5*exp(2/5*t)
11
>> syms s
>> ilaplace (5/((s^2)+49))
ans = 5/49*49^(1/2)*sin(49^(1/2)*t)
12
>> syms s
>> ilaplace ((10*s)/((s^2)+16))
ans = 10*cos(16^(1/2)*t)
13
>> syms s
>> ilaplace ((4*s)/((4*(s^2))+1))
ans = cos(1/2*t)
14
>> syms s
>> ilaplace ((1)/((4*(s^2))+1))
ans = 1/2*sin(1/2*t)
15
>> syms s
>> ilaplace ((1)/(((s^2))-16))
ans = -1/16*(-16)^(1/2)*sin((-16)^(1/2)*t)
16
>> syms s
>> ilaplace ((10*s)/(((s^2))-25))
ans = 10*cos((-25)^(1/2)*t)
17
>> syms s
>> ilaplace (((2*s)-6)/(((s^2))+9))
ans = 2*cos(3*t)-2*sin(3*t)
18
>> syms s
>> ilaplace (((s)-1)/(((s^2))+2))
ans = -1/2*2^(1/2)*sin(2^(1/2)*t)+cos(2^(1/2)*t)
19
>> syms s
>> ilaplace ((1)/(((s^2))+(3*s)))
ans = 1/9*9^(1/2)*(exp((-3/2+1/2*9^(1/2))*t)-exp((-3/2-1/2*9^(1/2))*t))
20
>> syms s
>> ilaplace (((s)+1)/(((s^2))-(4*s)))
ans = -1/4+5/4*exp(4*t)
21
>> syms s
>> ilaplace (s/((s^2)+(2*s)-(3)))
ans = 3/4*exp(-3*t)+1/4*exp(t)
22
>> syms s
>> ilaplace (1/((s^2)+(s)-(20)))
ans = 1/81*81^(1/2)*(exp((-1/2+1/2*81^(1/2))*t)-exp((-1/2-1/2*81^(1/2))*t))
23
>> syms s
>> ilaplace ((0.9*s)/((s-0.1)*(s+0.2)))
ans = 3/5*exp(-1/5*t)+3/10*exp(1/10*t)
24
>> syms s
>> ilaplace ((s-3)/((s-(3^(1/2)))*(s+(3^(1/2)))))
ans = -1/2*exp(3^(1/2)*t)*3^(1/2)+1/2*exp(3^(1/2)*t)+1/2*exp(-3^(1/2)*t)*3^(1/2)+1/2*exp(-3^(1/2)*t)
25
>> syms s
>> ilaplace ((s)/((s-2)*(s-3)*(s-6)))
ans = 1/2*exp(2*t)-exp(3*t)+1/2*exp(6*t)
26
>> syms s
>> ilaplace (((s^2)+1)/((s-1)*(s+1)*(s-2)*s))
ans = -exp(t)-1/3*exp(-t)+5/6*exp(2*t)+1/2
27
>> syms s
>> ilaplace (((2*s)+4)/((s-2)*((s^2)+(4*s)+3)))
ans = 8/15*exp(2*t)-1/5*exp(-3*t)-1/3*exp(-t)
28
>> syms s
>> ilaplace ((s+1)/(((s^2)-(4*s))*(s+5)))
ans = -1/20+5/36*exp(4*t)-4/45*exp(-5*t)
29
>> syms s
>> ilaplace ((1)/(((s^2)+(4))*(s^2)))
ans = 1/16*4^(1/2)*(4^(1/2)*t-sin(4^(1/2)*t))
30
>> syms s
>> ilaplace ((s-1)/(((s^2)+(1))*(s^2)))
ans = -t+1-cos(t)+sin(t)
31
>> syms s
>> ilaplace ((s)/(((s^2)+(4))*(s+2)))
ans = -1/4*exp(-2*t)+1/4*cos(2*t)+1/4*sin(2*t)
32
>> syms s
>> ilaplace ((1)/(((s^4)-9)))
ans = -1/18*2^(1/2)*(-9)^(1/4)*(sin(1/2*2^(1/2)*(-9)^(1/4)*t)*cosh(1/2*2^(1/2)*(-9)^(1/4)*t)-cos(1/2*2^(1/2)*(-9)^(1/4)*t)*sinh(1/2*2^(1/2)*(-9)^(1/4)*t))
33
>> syms s
>> ilaplace ((1)/(((s^2)+1)*((s^2)+4)))
ans = 1/3*sin(t)-1/6*sin(2*t)
34
>> syms s
>> ilaplace (((6*s)+3)/(((s^2)+1)*((s^2)+4)))
ans = 2*cos(t)+sin(t)-2*cos(2*t)-1/2*sin(2*t)
