1. Mathematics
2. Calculus and Analysis
3. 28505

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Three problems regarding the Wronskian and solutions of a second order differential equation.
Example of a question

1. Determine whether the following sets of functions are linearly dependant or independent... Please see attached.

2. Bessel's equation x²y" + xy' + (x² - n²)y = 0
where n is a constant, is an important differential equation that arises, for example, in the study of the vibrations of a circular drumhead.

a) Let y1(x) and y2(x) be any two solutions to Bessel's equation. Without computing y1 and y2, determine their Wronskian.

b) One solution to (1) with n=1/2 is sinx/sqrt(x) Find a second linearly independent solution.

c) Compute the Wronskian for the two solutions you found in part (b).

Please see attached for full question.