Question

5. The equation axy is known as the Airy equation in honor of G. B. Airy a British astronomer who studied it in 1838 as a simple model to explain diffraction of light. Here are the plots of two solutions named as Ai(x), B(x) dx2 Aix) Bi(x) 0.00 0.25 -13 These solutions do not have a closed form (like cos(x)) Instead, they have a representation in series (2.3)(5 6)(8.9) (3k - 1)3k) 3k+1 Bi(x)x+ 4)67)(9-10)..(3k)(3k+ 1)) Either from the graphs of the series representation, show that these 2 solutions are linearly independent. Remember, this is answered from the Wronskian, which is either always zero (for linear dependence) or never zero (for linear independence). Explain your answer. Writing something along the lines "they are linearly independent because there are different" in not the way to go. The functions y1(x)-cos(x), y2(x)-2cos(x) are different but NOT linearly independent

Answer 1

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(2 41

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