- #1
JulieK
- 50
- 0
I have the following differential equation which I obtained from Euler-Lagrange
variational principle
\frac{\partial}{\partial x}\left(\frac{1}{\sqrt{y}}\frac{dy}{dx}\right)=0
I also have two boundary conditions: y\left(0\right)=y_{1} and
y\left(D\right)=y_{2} where D, y_{1} and y_{2} are known
numbers.
I assume that I should integrate once to get
\frac{1}{\sqrt{y}}\frac{dy}{dx}=f\left(y\right)
where f\left(y\right) is a function of y. I would like to get
y as a function of x but the problem is that I don't know the
form of f\left(y\right).
My question, how to solve this equation to get y as a function
of x. Is it possible to guess the form of f\left(y\right), e.g.
from the bounday conditions.
variational principle
\frac{\partial}{\partial x}\left(\frac{1}{\sqrt{y}}\frac{dy}{dx}\right)=0
I also have two boundary conditions: y\left(0\right)=y_{1} and
y\left(D\right)=y_{2} where D, y_{1} and y_{2} are known
numbers.
I assume that I should integrate once to get
\frac{1}{\sqrt{y}}\frac{dy}{dx}=f\left(y\right)
where f\left(y\right) is a function of y. I would like to get
y as a function of x but the problem is that I don't know the
form of f\left(y\right).
My question, how to solve this equation to get y as a function
of x. Is it possible to guess the form of f\left(y\right), e.g.
from the bounday conditions.
