First Order Linear Equations

Purpose:

To solve linear first order differential equations using a CAS. We also study these equations graphically.

Description:

The variation of parameter formula for first order linear differential equations is developed. Students are asked to create a worksheet which uses the formula to solve a generic first order linear differential equation. This worksheet must also check that the function found is the solution.

Students do the following for each of set of given initial value problems.

• Graph the direction field.
• By hand, sketch the solution of the differential equation which passes through the given initial point (x₀, y₀) using the direction field.
• Use their worksheet to find the solution of the initial value problems. Verify your solutions.
• Sketch the actual solution along with the direction field on a separate graph. Comment on how well the solution sketched by hand corresponds to the actual solution.
• Compare the intervals for which p(x) and g(x) are defined to the interval on which the graph of the solution exists.

Return to Differential Equations: Explorations Through Technology.