y^{''}-2y^'-3y=4t

解答

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 t

y = c_{1} e^{3 t} + c_{2} e^{- t} - \frac{4 t}{3} + \frac{8}{9}

求解步骤

y^{''} (t) - 2 y^{'} (t) - 3 y = 4 t

求解线性方程:

y = c_{1} e^{3 t} + c_{2} e^{- t} - \frac{4 t}{3} + \frac{8}{9}

y = c_{1} e^{3 t} + c_{2} e^{- t} - \frac{4 t}{3} + \frac{8}{9}

y^{^{''}} + 4 y^{^{'}} = sin (2 x)

(D^{2} + 13 D + 13) x = 12 t^{2} + 2 t - cos (t)

y^{^{''}} - 6 y^{^{'}} + 9 y = t, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - y = x e^{\frac{x}{2}}

y^{^{''}} + 9 y = e^{2 x} + x^{2} sin (x)