How do you find the general solution of PDE?
How do you find the general solution of PDE? uxx = −u, which, as an ODE, has the general solution u = c1 cosx + c2 sinx. Since the constants may depend on the other variable y, the general solution of the PDE will be u(x, y) = f(y) cosx + g(y) sinx, where f and g are arbitrary functions. Which equation is hyperbolic? We will classify these equations into three different categories. If b2 − 4ac > 0, we say the equation is hyperbolic. If b2 − 4ac = 0, we say the equation is parabolic. If b2 −...