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1. How to find the area of an n-dimensional triangle?

1. Homework Statement How to find area of an n-dimensional triangle using vectors? 2. Homework Equations 3. The Attempt at a Solution
2. Why do 2nd-order linear ODEs have at most two independent solutions?

1. Homework Statement Why does the following ODE ALWAYS have two linearly independent solutions? x''(t) + a(t) x'(t) + b(t) x(t) = f(t) The characteristic polynomial argument is not sufficient?
3. Simple Lagrangian for constrained motion - please give your input

Hello fellow PF members I was wondering how one would go about finding the lagrangian of a problem like the following: A particle is constrained to move along the a path defined by y = sin(x). Would you simply do this: x = x y = sin(x) x'^2 = x'^2 y'^2 = x'^2 (cos(x))^2...
4. How do I solve this differential equation?

1. Homework Statement Solve the following differential equation: 2. Homework Equations 2 y (y'')^2 + 2 y y''' y' -2 (y')^2 y'' = - (y')^2 3. The Attempt at a Solution I don't know if the following is useful, but if you divide both sides by y^2, the LHS of the above...