Classification of second-order PDEs
General · Mathematics
Study notes
Q: Classify u_xx+4u_xy+3u_yy = 0. A = 1, B = 4, C = 3. B²-4AC = 16-12 = 4 > 0. HYPERBOLIC! Factor: (∂_x+∂_y)(∂_x+3∂_y)u = 0. Characteristics: dy/dx = 1, 1/3: ξ = x-y, η = 3x-y... solve: u = f(x-y)+g(3x-y)! (Wave-like: two families!)