How to simplify/solve this differential equation

I have the following equation

where is a function of (say ) and is a function of (say ). Are there any conditions under which becomes identically zero and hence this equation can be reduced to the follwoing form which is easier to solve:

If such condtions do not exist, what is the best and easiest method to solve the original equation?

Re: How to simplify/solve this differential equation

If m= f(y) and y= g(x), then so the answer to your question is "No". That product will be 0 if and only if at least one of or is 0- in other words if m is NOT a function of y or y is NOT a function of x. Your real problem is that you have **two** "unkowns", m as a funciton of y and y as a function of x, but only one equation.

Re: How to simplify/solve this differential equation

Many thanks!

I have two equations not just one because I know f(y) and I want to find g(x) which is the function of interest to me.

Re: How to simplify/solve this differential equation

I also wish to know if this equation can be solved numerically for g(x) if analytical solution is not possible.