# How Do I Find the Exact solution after using the Finite Difference Method?

My starting equation is $$y'' = \frac{wx}{2EI}(L-x)$$ [Beam Formula]

I got my approximations, but how do I use that to find the exact equation? I know that y = y(homogeneous) + y(particular).

But the homogeneous solution would come from $$y'' = 0$$. How do I even use that to find the homogeneous solution with my characteristic equation?

Also, I find that my particular solution is also zero. (Guessing that the answer to: $$y'' = 0$$ is $$y1 = y2 = 0$$.)

Help, thanks.

• Your expressions are hard to read. Please use MathJax. As for the question (if I understand it correctly), in general an approximation doesn't help you find the exact solution. Hence, it is used when no exact solution is available. Otherwise, why even use a numerical method? – Yuriy S Nov 23 '18 at 0:29
• Yeah I'm trying to use numerical methods. I don't know which one to use. – Jackie Nov 23 '18 at 0:29
• Your title says "finite differences", I assume this is the method you wanted to use? Honestly, I'm not sure what you are asking – Yuriy S Nov 23 '18 at 0:31
• This method is what I'm referring to: mathforcollege.com/nm/mws/gen/08ode/… I cant understand what he does on page five to solve for his homogeneous solution – Jackie Nov 23 '18 at 0:32
• Are you trying to solve the equation (E.1.1)? Cause that is not the equation you have written in this question. You missed a term – Yuriy S Nov 23 '18 at 0:39