How to Determine Linear Dependence Using Wronskian: A Quick Guide

[GreatEscapist]

urgent Diff. Eqs. Wronskian question

Homework Statement

See attached image- it's a lot easier.

Homework Equations

We know that when the wronskina = 0, it is linearly dependent on most points, and if it is not equal to 0, then the solutions form a fundamental set of solutions because they are linearly independent on all points.

The Attempt at a Solution

I am confused because it doesn't give solutions, just the initial values...do i have to go and FIND each solution (3) by order or reduction or something? Why did it give me those initial values?

Quick help is much appreciated.

 

[Dick]

No, you don't have to compute the solutions. They gave you the initial values so you could compute the wronskian at x=0. That tells you something about linear independence. And you can also use them for the second part to figure which combination of y1, y2 and y3 will give you y. Write y(x)=a*y1(x)+b*y2(x)+c*y3(x). Figure out what a, b and c are.

 

[GreatEscapist]

Figured it out, thanks!