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Planar Systems

Two distinct real eigenvalues of A give the general solution of x' = Ax as exponentials growing or decaying along each eigenvector direction.

The ODE Project, Planar Systems

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10 exercises

Exercise 1

Find the general solution of each of the linear systems in Solving Linear Systems with Distinct Real Eigenvalues.

2.5

Exercise 2

Find the general solution of each of the linear systems in Solving Linear Systems with Distinct Real Eigenvalues.

2.5

Exercise 3

Find the general solution of each of the linear systems in Solving Linear Systems with Distinct Real Eigenvalues.

2.5

Exercise 4

Find the general solution of each of the linear systems in Solving Linear Systems with Distinct Real Eigenvalues.

2.5

Exercise 5

Solve each of the following linear systems for the given initial values. in Solving Initial Value Problems.

2.5

Exercise 6

Solve each of the following linear systems for the given initial values. in Solving Initial Value Problems.

2.5

Exercise 7

Solve each of the following linear systems for the given initial values. in Solving Initial Value Problems.

2.5

Exercise 8

Solve each of the following linear systems for the given initial values. in Solving Initial Value Problems.

2.5

Exercise 10

Consider the linear system

Find the general solution of the homogeneous system
Find a particular solution for
Find the solution of

Exercise 12

Prove that is the general solution of

Adapted from The ODE Project © 2019–2025 Thomas W. Judson. Licensed under CC BY 4.0. Source: The ODE Project. Imported at revision 7935458.