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I am trying to reduce the following ODE to Bessel's ODE form and solve it:
$$x^{2}y''(x)+x(4x^{3}-3)y'(x)+(4x^{8}-5x^{2}+3)y(x)=0\tag{1} \, .$$
I tried to solve it via the standard method, i.e., by comparing it with a generalised ODE form and finding the solution from then on. The general form (...
The parametric equation
$$\begin{align*}
x(t) &= \cos t\\
y(t) &= \sin t
\end{align*}$$
traces the unit circle centered at the origin ($x^2+y^2=1$). Similarly,
$$\begin{align*}
x(t) &= \cosh t\\
y(t) &= \sinh t
\end{align*}$$
draws the right part of a regular hyperbola ($x^2-y^2=1$). The ...
The proposition in probability theory known as the law of total expectation, the law of iterated expectations, the tower rule, the smoothing theorem, and Adam's Law among other names, states that if X is an integrable random variable (i.e., a random variable satisfying E( |X| ) < ∞) and Y is any random variable, not necessarily integrable, on the same probability space, then
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