4q^{''}+8q^'+80q=88t

解答

4 q^{^{''}} + 8 q^{^{'}} + 80 q = 88 t

q (t) = e^{- t} (c_{1} cos (19 t) + c_{2} sin (19 t)) + \frac{11 t}{10} - \frac{11}{100}

求解步骤

4 q^{''} (t) + 8 q^{'} (t) + 80 q (t) = 88 t

求解线性方程:

q (t) = e^{- t} (c_{1} cos (19 t) + c_{2} sin (19 t)) + \frac{11 t}{10} - \frac{11}{100}

q (t) = e^{- t} (c_{1} cos (19 t) + c_{2} sin (19 t)) + \frac{11 t}{10} - \frac{11}{100}

3 y^{^{''}} - 8 y^{^{'}} - 3 y = 5

y^{^{''}} + 4 y^{^{'}} - 5 = 2 t^{2} - 3 t + 6

y^{^{''}} + 25 y = 6 x, y (0) = 1, y^{^{'}} (0) = 5

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = e^{t} (t^{2} + sin (t))

y^{^{''}} + 16 y = 3, y (0) = 0, y^{^{'}} (0) = 0