MATH 4B Lecture Notes - Lecture 8: Wronskian, Superposition Principle, Linear Algebra

• School: UCSB
• Department: Mathematics
• Course: MATH 4B
• Professor: Wei

Document Summary

Second order linear homogenous ode with constant coefficients: By substitution, we"ve seen that will be a solution is a root of the characteristic equation. The nature of the roots depends on the discriminant. Is there a function so that ? is called the variation of parameter. To check if and is a basis, compute the wronskian. The general solution of , when is , Superposition principle: suppose that and are solutions of the second order. Then any linear combinations of and are also solutions. If and are solutions whose wronskian , then represent a. The general solution of the homogenous equation above is for arbitrary constants. Suppose that is some (particular) solution of the inhomogeneous equation. Suppose the is the general solution of the homogeneous equation. Review of homogeneous case fundamental set of solutions linear homogenous ode. Same as for systems of linear equations in linear algebra.