A Bessel's Differential Equation That We Can Actually Solve x^2y''+xy'+(x^2-1/4)y=0
Hearing the words Bessel differential equation is enough to make most advanced calculus students close their textbooks in panic. We are conditioned to believe that these equations can only be solved using infinite power series with recurrence relations. However, when the order is precisely one-half, the entire structure simplifies into something wonderfully manageable. Here is the elegant substitution that reveals an explicit, closed-form solution with ultimate satisfaction.Get my practice exam on 2nd order differential equations: https://www.patreon.com/blackpenredpen/posts/differential-2-174732541
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