Solving differential equation from variational principle
I have the following differential equation which I obtained from Euler-Lagrange
I also have two boundary conditions: and
where , and are known
I assume that I should integrate once to get
where is a function of . I would like to get
as a function of but the problem is that I don't know the
form of .
My question, how to solve this equation to get as a function
of . Is it possible to guess the form of , e.g.
from the bounday conditions.
Re: Solving differential equation from variational principle
Since y is a function of x, then f(y) is function of x. It's derivative is 0, hence f(y)=constant.
Then, solve dy/dx=c*sqrt(y), which is a separable ODE.