Linear Algebra : Wronskian

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• Wronskian - linear independence

  79433 Wronskian- Linear independence of functions Three functions e^x, sinx and cosx are given. They must be shown linear independent by using Wronskian. Using the Determinant definition of Wronskian for functions, the problem is solved.

• Linear Dependency, Wronskian and Bessel's Equation

  28505 Linear dependency, Wronskian and Bessel's Equation Three problems regarding the Wronskian and solutions of a second order differential equation. Example of a question 1.

• Continuous Functions, Fundamental Set of Solutions and Coefficient Functions

  The criterion to establish if a set of solutions is fundamental (that means contains only linear independent functions) is the Wronsky's determinant (or wronskian):

• Systems of Ordinary Differential Equations

  Find the eigenvalue(s) of A by solving |λ-A|=0 Solve the linear equation (λ-A)u=0 to get the eigenvector(s) u= 〖[u_1,u_2]〗^2 Find the fundamental matrix Φ(t) What is the Wronskian for Φ?

• Differential Equations : Rate of Change Application Problem and Wronskian

  We can easily see that, Cos (2x) = 1 + (-2)*Sin^2(x) so one function can be expressed as a linear combination of the other two functions. A Rate of Change Application Problem and Wronskian are solved . The solution is detailed and well presented.

• Normed Linear Space : Hahn-Banach Theorem

  37040 Initial-Value Problems, Wronskian and Particular Solutions Suppose that E is a normed linear space. Prove that if E* is separable, then E is separable. **See attachment for complete problem. Thanks!

• Linear dependence of solutions

  28803 Linear dependence of solutions One solution to ty"-(t+2)y'+2y=0 is exp(t) Find a second linearly independent solution. Hi there! Here is the solution in two file formats as usual.

• Finding an Independent Solution to a Second Order ODE

  We use Abel's identity to compute the Wronskian of a given second order linear ODE, which we then use to compute a solution linearly independent of a given one.

• Wronskian of Functions

  Define the Wronskian of functions.