Solving ODEs Symbolically

Ordinary Differential Equations

ODE =

solving an ODE =

ordinary
    vs.
partial

first-order =

Steady-state of an ODE

steady-state =

To find the steady-state:

Example:

Linear First-Order ODEs

linear first-order ODE =

Which of the following examples are linear first-order ODEs?

1. dy(t)/dt = 3y(t)

2. dp(t)/dt = αp(t)^1/2

3. dq(t)/dt = 1/q(t)

4. dr(t)/dt = 3sin(t)²r(t)

5. ds(θ)/dθ = sin(s(θ))

Solving Linear First-Order ODEs By Hand

First, re-write ODE in form:

Solution is:

Example

Solving Linear First-Order ODEs Using Maple

General procedure

• construct the ODE

• enter the ODE symbolically

• use dsolve to solve the ODE symbolically

• substitute values for symbolic constants

• explicitly plot the solution function