How the Discriminant Determines the Solution Form

Homogeneous Second-Order Differential Equations

11th Grade·Math·UK A-Level

Updated 1 month ago · 4 views

Explain how the sign of the discriminant of the auxiliary equation determines the form of the complementary function.

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Homogeneous Second-Order Differential Equations

11th Grade · Math · UK A-Level

7 lessons

Goal

Solve homogeneous second-order linear differential equations with constant coefficients by forming the auxiliary equation and relating the discriminant to the form of the solution.

7 lessons

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Introduction to Second-Order Linear Differential EquationsUp next
The Auxiliary EquationNot started yet
Solving the Homogeneous Case: Real Distinct RootsNot started yet
Solving the Homogeneous Case: Repeated RootNot started yet
Solving the Homogeneous Case: Complex RootsNot started yet
How the Discriminant Determines the Solution FormYou are here
Homogeneous Second-Order DEs: Fluency PracticeNot started yet

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Learning standards covered

FM-I6General Certificate of Education Advanced Level (UK A-Level) · Further-maths · 11th Grade

Understand and use the relationship between the cases when the discriminant of the auxiliary equation is positive, zero and negative and the form of solution of the differential equation