Georgia HomeroomDE.AR.3Higher-Order DE Applications
Solve contextual, mathematical problems involving second and higher order differential equations to explain real-life phenomena.
Appears in: Mathematics, High School
Expectations
Solve and use second and higher order differential equations.
DE.AR.3.1Determine 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.3.2Solve 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.3.3Solve second-order differential equations that apply to various real-world models.
DE.AR.3.4Use vector function notation when discussing the structure of solution sets for homogeneous systems as it pertains to the Wronskian.
DE.AR.3.5Determine 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.3.6Determine 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.3.7Solve higher-order constant coefficient homogeneous differential equations.
DE.AR.3.8Solve special case non-homogeneous second order ordinary differential equations including Cauchy-Euler Equations.
DE.AR.3.9Find 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.3.10Determine ordinary points, recurrence relations, and change the index as they relate to series solutions to ordinary differential equations.
DE.AR.3.11Find series solutions to first and second-order non-linear initial value problems.
Georgia Milestones coverage
No Georgia Milestones blueprint cites this standard.