y^{''}-10y^'+21y=e^{7t}

解答

y^{^{''}} - 10 y^{^{'}} + 21 y = e^{7 t}

y = c_{1} e^{7 t} + c_{2} e^{3 t} + \frac{e ^{7 t} t}{4}

求解步骤

y^{''} (t) - 10 y^{'} (t) + 21 y = e^{7 t}

求解线性方程:

y = c_{1} e^{7 t} + c_{2} e^{3 t} + \frac{e ^{7 t} t}{4}

y = c_{1} e^{7 t} + c_{2} e^{3 t} + \frac{e ^{7 t} t}{4}

y^{^{''}} + 7 y^{^{'}} + 10 = x

y^{^{'''}} - 16 y^{^{'}} = t e^{- 4 t}

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 3

y^{^{''}} - y^{^{'}} = 1 + e^{x}