desolve_system

## Description

We can use `desolve_system` to obtain a symbolic solution to the system of differential equations

\begin{align} \frac{dx}{dt} & = 3x + 4y \\ \frac{dy}{dt} & = x. \end{align}

## Sage Cell

#### Code

```
t = var('t')
x = function('x')(t)
y = function('y')(t)
de1 = diff(x,t) == 3*x + 4*y
de2 = diff(y,t) == x
desolve_system([de1, de2], [x,y])
```

## Options

#### Option

We can use `desolve_system` to obtain a symbolic solution to the initial-value problem

\begin{align} \frac{dx}{dt} & = 3x + 4y \\ \frac{dy}{dt} & = x \\ x(0) & = 1 \\ y(0) & = -2. \end{align}

#### Code

```
t = var('t')
x = function('x')(t)
y = function('y')(t)
de1 = diff(x,t) == 3*x + 4*y
de2 = diff(y,t) == x
desolve_system([de1, de2], [x,y], ics=[0,1,-2])
```

## Tags

Primary Tags: Differential Equations: Systems of differential equations.

Secondary Tags: Systems of differential equations.

## Related Cells

None

## Attribute

Permalink:

Author: T. W. Judson

Date: 15 Mar 2019 17:17

Submitted by: Tom Judson