Equações Resumo Área 3

* Tipos de equações\n\n1) Cauchy-Euler: [f''(y) + a(y)f'(y) + b(y)f(y) = 0] – γ = Cf', Df''\n\nEr negro: -α(α-1)f'γ + b(y) = 0 → –γ = Cf', Df''\n\nSe α = α1, α2, ...\n\nSe α0 = 0, γ = Cf'', Df' = f.\n\nSe α = α1, α2, ...\n\n2) Legendre: [1(x-y)²γ''(y) - 2γ'y' + p(y)γ = 0] p ∈ R e com ramo\n\nP0 = 1/n² = d²γ/ dγ² \n\n(forma geral)\n\nF(x) = ∑α_0Pn,γ(γ) = ∑γ(∂γ/∂x)\n\n3) Bessel: [x²y'' + xy' + (x² - p²)y = 0]; {m ∈ P}\n\nF(y) = n derivadas em be\n\nJ0(x) = ∑(−1)n/(n!)²(n - m)\n\n1) Se p ∈ Z; Y(α) = C1 Jp(x) + C2 Jp(x)\n\nL.I.\n\n2) Se p ∈ Z, Im(x) = (−1) * Yp(γ - 1) Jm(x)\n\nJ = Jm, e J\n\nγ = C1 Jp(x) + C2 Yp(x) = Yγ ∈ JmL² 3) Bessel\n\nPropriedades: 1) Jp(m) F0 → Jm(x) = Im(x) (m ∈ R+, com x)\n\nJ1 > 1:\n\ndJ/ dH J(α) = p²Jp(k) → d(1J/ p)\n\n= J1 = Jn = (x/cos);\n\nJ1 = 2π/ /R\n\nJ0(α) = ∑ A_n Jm (σ_m,ν)\n\nAm = 2/∫(σ_0, Jm(α_m,ν) s(y)\ndy\n\nα_m ∈ | fixed)\n\n* Séries de Fourier-Bessel:\n\n(y) = ∑[Am Jn(α_m,x) = Jp(x, x - Xα): m\n\nF(x) = 0 → p0 \n\nP0 = R0 = Rm*\n\nR(x - x0) P0... R(X)\n\nmass enfrentar X = (X0 - X)\n\nR_0 ∈ pro variáveis de x\n\nAnalisando Frobenius:\n\nγ(ω) = (X-X_0) ∑(−1)n Amn(X-X0)n\n\n0 = 0? 0 {}