desolve

## 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: