---
title: "DE.AR.4: Systems of Differential Equations (Georgia Mathematics standard)"
code: DE.AR.4
cite_as: Georgia Standards of Excellence, Mathematics, DE.AR.4
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/DE.AR.4
md_url: https://georgiahomeroom.org/standards/code/DE.AR.4.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/DE.AR.4.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# DE.AR.4: Systems of Differential Equations

Solve contextual, mathematical problems involving systems of differential equations to explain real-life phenomena.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- **DE.AR.4.1**: Determine whether a contextual situation results in a system of differential equations and apply the basic existence and uniqueness results for the corresponding initial value problems.
- **DE.AR.4.2**: Solve constant coefficient homogeneous systems using eigenvalues and eigenvectors. Solve systems with real, distinct eigenvalues, as well as those with repeated and imaginary eigenvalues.
- **DE.AR.4.3**: Draw phase portraits for solutions of homogeneous systems with constant coefficients.
- **DE.AR.4.4**: Solve non-homogeneous systems of ordinary differential equations using the method of undetermined coefficients and variation of parameters.
- **DE.AR.4.5**: Determine which non-linear systems are locally linear and identify the behavior of the system about each critical point.
- **DE.AR.4.6**: Plot locally linear systems.
- **DE.AR.4.7**: Use population models derived from locally linear systems.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.