TITLE: Analytical solution for coupled ODE system
QUESTION [5 upvotes]: I came across this coupled system of ODE in my research (related to foulant in reaction diffusion system):
$$\frac{d^2y}{dx^2} - A\frac{yz}{x} = 0$$
$$\frac{d^2z}{dx^2} - B\frac{yz}{x} = 0$$
where $A$ and $B$ are constants. Can it be solved analytically?

REPLY [5 votes]: Mathematica cannot solve this system of ODEs, even after the decoupling suggested by user LeechLattice, even with $\alpha=\beta=0$ and $A=1$. This means that the existence of an explicit solution is highly unlikely.
Here is the image of the corresponding Mathematica notebook: