lesson
Solving the Homogeneous Case: Complex Roots
Write the general solution y = e^(αx)(A cos βx + B sin βx) when the auxiliary equation has complex roots.
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Homogeneous Second-Order Differential Equations
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 RootsYou are here
- How the Discriminant Determines the Solution FormNot started yet
- Homogeneous Second-Order DEs: Fluency PracticeNot started yet
Learning standards covered
FM-I4General Certificate of Education Advanced Level (UK A-Level) · Further-maths · 11th GradeSolve differential equations of form y''+ay'+by=0 where a and b are constants by using the auxiliary equation
FM-I6General Certificate of Education Advanced Level (UK A-Level) · Further-maths · 11th GradeUnderstand 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