just having a bit of trouble with using the method of reduction of order to find a solution to the equation:
2(x^2)y′′ + 3xy′− y = 0 x > 0
all help is greatly appreciated!
What "reduction of order" method are you talking about? The ones I know require that you already know one solution to the equation.
This is, in any case, an "Euler type" or "equipotential" equation. Trying a solution of the form $\displaystyle y= x^r$ may lead to a solution.