There's this problem that's asking me to use Euler's equidimensional equation, which is a second order differential equation. The problem tells me to substitute x = exp(z) to transform the equation into one with constant coefficients, and apply the technique to various examples.
Just to illustrate, Euler's equidimensional equation looks like this:
(x^2)*y'' + p*x*y' + q*y = 0, where p and q are constants. One of my tasks is to use the substitution x = exp(z) to solve the following problem:
(x^2)*y'' + 3*x*y' + 10*y = 0
Anyone have an idea how to use the substitution to my advantage? Just inserting exp(z) for x doesn't work. Should I be changing y' to be in terms of z?
Any help appreciated, thanks.