Description
desolve will compute the “general solution” to a 1st or 2nd order ordinary differential equation using Maxima. To solve the equation $x′+x−1=0$.
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 - 1
desolve(DE, [x,t])
Options
Option
You can use ics to specify an initial condition. For example, we can solve the initial value problem $x′+x−1=0$ with $x(0) = 2$.
Code
t = var('t')
x = function('x')(t)
DE = diff(x, t) + x - 1
desolve(DE, [x,t],ics=[0,2])
Option
Higher order equations such as second-order linear equations can be solved. The following commands solve $x'' + 2x' + x =\sin t$.
Code
t = var('t')
x = function('x')(t)
DE = diff(x,t,2)+2*diff(x,t)+x == sin(t)
desolve(DE, [x,t])
Option
We can specify initial conditions for second-order linear equations. The following commands solve $x'' + 2x' + x =\sin t$, $x(0) = 1$, $x'(0) = 0$.
Code
t = var('t')
x = function('x')(t)
DE = diff(x,t,2)+2*diff(x,t)+x == sin(t)
desolve(DE, [x,t], ics=[0, 1, 0])
Option
Implicit solutions are returned for separable differential equations. Consider the solution to $\cos x \dfrac{dy}{dx} = \tan x$.
Code
x = var('x')
y = function('y')(x)
DE = diff(y,x)*cos(y) == tan(x)
desolve(DE, [y,x])
Tags
Primary Tags: Differential Equations
Secondary Tags:
Related Cells
- 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.
- desolve_laplace. Solving ordinary differential equations using Laplace transforms.
- Interact to plot direction fields and solutions for first order differential equations. A Sage interact for plotting direction fields for differential equations.
Attribute
Permalink:
Author: http://doc.sagemath.org/html/en/reference/calculus/sage/calculus/desolvers.html
Date: 08 Jul 2017 14:10
Submitted by: Tom Judson