Recent content by mbp

Multiply both sides for dx getting g(f(x)) f'(x) dx = g(x) dx Then integrate both sides G(f(x)) = G(x) where G is a primitive of g, and you get f(x) = x as pasmith suggested

It looks like you can apply separation of variables and integrate

In classical mechanics the Hamiltonian is a function of the (generalized) coordinates and momenta. The energy is fixed by the initial conditions \begin{equation} E = H(x(0),y(0)) \end{equation} Starting from x(0), y(0) the system evolves along the curve H(x(t),y(t)) = E for all t. The...

The solution given by JJacquelin is correct. In fact your system is conservative, it can be written as a system of first order ODE \begin{eqnarray} x' & = & y \\ y' & = & \frac{-b}{x} + a \end{eqnarray} Divide one equation by the other to get \begin{equation} \frac{dy}{dx} = \frac{-b/x +...

It is not necessary to compute eigenvectors. This system is Hamiltonian (conservative). On dividing one equation by the other you get \begin{equation} \frac{dx}{dy} = \frac{y^2}{x^2} \end{equation} Separating variables and integrating you find the Hamiltonian \begin{equation} H(x,y) =...

Hello to everyone. I am new with this forum and I am asking help with PDE. I have a linear PDE: L f(x,y,t) = 0 where L is a second order linear operator depending on x, y, their partial derivatives, and t, but not on derivatives with respect to t. The question...