sympy.integrals.inverse_laplace_transform() in python

With the help of inverse_laplace_transform() method, we can compute the inverse of laplace transformation of F(s).

Syntax : inverse_laplace_transform(F, s, t) 
Return : Return the unevaluated transformation function. 

Example #1 :
In this example, we can see that by using inverse_laplace_transform() method, we are able to compute the inverse laplace transformation and return the unevaluated function. 

Python3

# import inverse_laplace_transform
from sympy.integrals.transforms import inverse_laplace_transform
from sympy import exp, Symbol
from sympy.abc import s, t

a = Symbol('a', positive = True)
# Using inverse_laplace_transform() method
gfg = inverse_laplace_transform(exp(-a * s)/s, s, t)

print(gfg)

Output :

Heaviside(-a + t) 

Example #2 :

Python3

# import inverse_laplace_transform
from sympy.integrals.transforms import inverse_laplace_transform
from sympy import exp, Symbol
from sympy.abc import s, t

a = Symbol('a', positive = True)
# Using inverse_laplace_transform() method
gfg = inverse_laplace_transform(exp(-a * s)/s, s, 5)

print(gfg)

Output :

Heaviside(5 – a) 

Example #3:

Python3

# import inverse_laplace_transform
from sympy.integrals.transforms import inverse_laplace_transform
from sympy import exp, Symbol, sin
from sympy.abc import s, t

a = Symbol('a', positive = True)
# Using inverse_laplace_transform() method
gfg = inverse_laplace_transform(1/(s**2 + a**2), s, 5)

print(gfg)

Output :

sin(5*a)/a