---
title: "DE.AR.3: Higher-Order DE Applications (Georgia Mathematics standard)"
code: DE.AR.3
cite_as: Georgia Standards of Excellence, Mathematics, DE.AR.3
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/DE.AR.3
md_url: https://georgiahomeroom.org/standards/code/DE.AR.3.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/DE.AR.3.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.3: Higher-Order DE Applications

Solve contextual, mathematical problems involving second and higher order differential equations to explain real-life phenomena.

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

## Expectations

- Solve and use second and higher order differential equations.
  - **DE.AR.3.1**: Determine whether a first- or second-order differential equation has a unique solution over a given interval by applying the Existence and Uniqueness Theorem.
  - **DE.AR.3.2**: Solve second-order linear homogeneous and non-homogeneous differential equations by finding characteristic equations, using the method of undetermined coefficients and variation of parameters.
  - **DE.AR.3.3**: Solve second-order differential equations that apply to various real-world models.
  - **DE.AR.3.4**: Use vector function notation when discussing the structure of solution sets for homogeneous systems as it pertains to the Wronskian.
  - **DE.AR.3.5**: Determine the existence and uniqueness of solutions for second-order linear differential equations, determine a fundamental set of solutions, and verify that two solutions form a fundamental set by taking the Wronskian.
  - **DE.AR.3.6**: Determine the structure of solution set to higher-order differential equations, apply the basic Existence and Uniqueness Theorem to higher-order differential equations, and use the generalizations of the Wronksian for higher order differential equations.
  - **DE.AR.3.7**: Solve higher-order constant coefficient homogeneous differential equations.
  - **DE.AR.3.8**: Solve special case non-homogeneous second order ordinary differential equations including Cauchy-Euler Equations.
  - **DE.AR.3.9**: Find a second linearly dependent solution using reduction of order when given a solution to a non-homogeneous second-order differential equation.
- Find and use series solutions.
  - **DE.AR.3.10**: Determine ordinary points, recurrence relations, and change the index as they relate to series solutions to ordinary differential equations.
  - **DE.AR.3.11**: Find series solutions to first and second-order non-linear initial value problems.

## 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.