Laplace Transforms

## Description

Sage can compute Laplace transforms. The Laplace transform of $t^2e^t - \sin t$ is computed as follows:

## Sage Cell

#### Code

```
s, t = var('s, t')
f = t^2*exp(t) - sin(t)
f.laplace(t,s)
```

## Options

#### Option

We can also compute the inverse Laplace transform of

(1)\begin{align} F(s) = -\frac{1}{s^2 + 1} + \frac{2}{(s - 1)^3}. \end{align}

#### Code

```
s = var("s")
t = var("t")
F = -1/(s^2 + 1) + 2/(s - 1)^3
F.inverse_laplace(s,t)
```

## Tags

Primary Tags: Differential Equations: Laplace transforms

Secondary Tags: Laplace transforms: Basic transformations, Inverse transformations

## Related Cells

- desolve_laplace. Solving ordinary differential equations using Laplace transforms.

## Attribute

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Author: Sage Tutorial v7.6

Date: 08 Jul 2017 15:15

Submitted by: Tom Judson