y^{''}+5y^'+6y=x^2

解答

y^{^{''}} + 5 y^{^{'}} + 6 y = x^{2}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} - \frac{5 x}{18} + \frac{19}{108}

求解步骤

y^{''} (x) + 5 y^{'} (x) + 6 y = x^{2}

求解线性方程:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} - \frac{5 x}{18} + \frac{19}{108}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} - \frac{5 x}{18} + \frac{19}{108}

y^{^{''}} + 9 y = e^{t}

y^{^{''}} + y^{^{'}} - 6 y = x

y^{^{''}} - 7 y^{^{'}} + a = 0, y (0) = 1, y^{^{'}} (0) = 10

y^{^{''}} + 4 y = - 6, y (\frac{π}{8}) = - \frac{1}{2}, y^{^{'}} (\frac{π}{8}) = 2

y^{^{''}} - 4 y^{^{'}} + 8 y = 8 x^{2} - 2