Laplace Calculator

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Laplace transform is a very useful method used in Calculus to solve given differential equations.Laplace

transform is an integral notation and the integral used to define it is an improper integral, with one of its limits

heading towards infinity. Laplace calculator is the quick online tool which can easily give the answers based

on Laplace transforms.

Example 1: Find the Laplace transform of the given function, f(t) = 2e^3t + 4e^-5t

<-Given function: 2e^3t + 4e^-5t

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

<-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

<-?(f(t)) = ?(2e^3t) + ?(4e^-5t)

<-?(f(t)) = 2/(s – 3) + 4/(s + 5)

Example 2: Find the Laplace transform of the given function, f(t) = e^6t -5e^-2t + 7

<-Given function: e^6t - 5e^-2t + 7

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

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

and if f(t) = 1 (constant) then <- ?(f(t)) = 1/s

<-Hence applying the above formulas to the given function, we get

<-?(f(t)) = ?(e^6t) - ?(5e^-2t) + ?(7)

<-?(f(t)) = 1/(s –6) -5/(s + 2) + 7(1/s)

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Laplace Calculator

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