desolve_laplace

## Description

desolve_laplace will solve an ordinary differential equation using Laplace transforms with or without initial conditions. The following commands solve $\dfrac{dx}{dt} - x = e^{-t}$.

## Sage Cell

#### Code

t = var('t')    # define a variable t
x = function('x')(t)   # define x to be a function of that variable
DE = diff(x, t) - x == exp(-t)
desolve_laplace(DE, [x,t])


## Options

#### Option

Solving the initial-value problem $\dfrac{dx}{dt} - x = e^{-t}$, $x(0) = 2$.

#### Code

t = var('t')    # define a variable t
x = function('x')(t)   # define x to be a function of that variable
DE = diff(x, t) - x == exp(-t)
desolve_laplace(DE, [x,t], ics=[0,2])


## Tags

Primary Tags: Differential Equations: Laplace transforms

Secondary Tags: Laplace transforms: Solving initial-value problems

## Attribute

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Date: 06 Jan 2018 20:03

Submitted by: Tom Judson

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