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how do I use the Wronskian method to show that f1(x) = sinh(ax) and f2(x) = cosh(ax) are linearly independent?
Oh, you use the definition of the Wronskian and if the determinant you get is non-zero, the solutions are linearly independent.
The first row will be f1, f2, and the second row will have f1' and f2'. Then the determinant is f1f2'-f2f1'
and it also includes a differential equation of y'' - a^2y = 0, I have to show that they are linearly independent for that equation
does that make sense?
Yeah, you can use the Wronskian to show that two solutions will be linearly independent. You would have obtained those solutions from the differential equation. Then you plug them into det(W) to see if they're independent.
The above expression I wrote out (that go cut off) equals -1, which is non-zero. Your solutions are linearly independent.
is this the only method, or easiest method, so solving these kind of questions? L.I equations?
Just one sec...distracted.
Are you sure the 'a' in the equation isn't a^2?
sorry - i just checked...off sick today
Haha uhh yes, its a^2
Re. your question about whether this is the easiest method to solve these equations: how are you exactly coming up with your solutions?
Or are you asking if this is the easiest way to show linear independence?
If it's the latter, I would say, 'yes'.
yes, I meant the latter
And okay, thanks! I am just learning this stuff, clearly. Newb
No probs. Increase my fan base - become a fan!
Sure thing, are you a professor? Incredibly smart student?
Little from column A, little from column B - postgrad.
Cool. Well I have no idea how to do anything on here, how do I become your fan?
And, why does everything I type show up five hundred times?
There should be a blue link next to my name that says, "Become a fan".
Next to a blue 'thumbs up' icon.
Try refreshing the page...I hear that works sometimes.
Ah well, I'll find it sometime, gotta get back to studying. Thanks for the help! I will become your fan asap. :) Appreciate it.
Ah! Found it
there. have a good one!