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

Related Cells

• desolve. Solving ordinary differential equations with desolve.
• desolve_odeint. Solving ordinary differential equations numerically with desolve_odeint.
• Euler's Method. eulers_method implements Euler’s method for finding a numerical solution of the first-order ODE $y′=f(x,y)$.
• Euler's Method for Systems. eulers_method_2x2 implements Euler’s method for finding a numerical solution of a $2 \times 2$ system of first-order ODEs.
• Laplace Transforms. Sage can compute Laplace transforms.
• Interact to plot direction fields and solutions for first order differential equations. A Sage interact for plotting direction fields for differential equations.

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Date: 06 Jan 2018 20:03

Submitted by: Tom Judson