The notation is etc...
Your solution idea is confusing as stated, what do you mean by take the derivative of the first one? Derivative with respect to what? You mean take ?
1. The problem statement, all variables and given/known data
Solve the following system of partial differential equations for u(x,y)
2. Relevant equations
3. The attempt at a solution
I am honestly not sure where to start, my lectures and tutorials this week have not been helpful at all. My guess is to take the derivative of the first equation and sub that into the second equation for y and then take the derivative of the second equation to get my final answer. But I am probably completely wrong. Any help or advice would be appreciated!
In , y can be treated as a constant: think of it as and separate: where, remember y is a constant. Integrate both sides to get . (Since "y is a constant", the constant of integration may be function of y, f(y).)
We can solve that for u as where . Since f(y) is an arbitrary function of y, so is F(y).
With that we can write which, since F cannot depend on x, requires that F(y)= 1 (so that F'(y)= 0).