I have to solve this as ODE...How can it be done ? u is a function of x and y but I do not have any idea how to transform this equation into derivative of one variable only
The problem can be written as and is a separable equation: . Integrating, so, taking the exponential of both sides, .
Finally, use the fact that we have been ignoring x- that is, treating it like a constant: the constant C' might be any function of x. If we call that "F(x)" then we have where F(x) is an arbitrary function of x, exactly the solution mr. fantastic got.