Laplace Transform Calculator

Laplace transform is the most commonly used transform in calculus to solve Differential equations. Laplace

transforms are used to reduce differential equations into algebraic expressions. Laplace transform calculator

is the online tool which can easily reduce any given differential equation into an algebraic expression as the

answer.



Example 1: Find the Laplace transform of the given function: f(t) = t³ – 7e^4t


Given function:t³ – 7e^4t

In order to find the Laplace transform for this function, we use the Standard Laplace formula:

If f(t) = tⁿ then <-Laplace transform of the function, ?(f(t)) = n!/ (sⁿ⁺¹)

If f(t) = e^at then <-Laplace transform of the function, ?(f(t)) = 1/s-a

Hence applying the above formula to the given function, we get

L (f(t)) = L (t³) - L (7e^4t)

L (f(t)) = 3!/s³⁺¹ - 7/(s – 4)

L (f(t)) = 6/s⁴ – 7/(s – 4)



Example 2: Find the Laplace transform of the given function: f(t) = t⁴ + 6e^2t – 5


Given function: t⁴ + 6e^2t – 5

In order to find the Laplace transform for this function, we use the Standard Laplace formula:

If f(t) = tⁿ then <- Laplace transform of the function, ?(f(t)) = n!/ (sⁿ⁺¹)

If f(t) = e^at then <-Laplace transform of the function, ?(f(t)) = 1/s-a

Hence applying the above formula to the given function, we get

   L (f(t)) = L (t⁴) + L (6e^2t) - L (5)

   L (f(t)) = 4!/s⁴⁺¹ +6/(s – 2) – 5(1/s)

   L (f(t)) = 24/s⁵+6/(s – 2) – 5/s