y^{'''}-8y^{''}+5y^'+y=5t

解答

y^{^{'''}} - 8 y^{^{''}} + 5 y^{^{'}} + y = 5 t

y = c_{1} e^{- 0.15883 \dots t} + c_{2} e^{0.86293 \dots t} + c_{3} e^{7.29589 \dots t} + 5 t - 25

求解步骤

y^{'''} (t) - 8 y^{''} (t) + 5 y^{'} (t) + y = 5 t

求解线性方程:

y = c_{1} e^{- 0.15883 \dots t} + c_{2} e^{0.86293 \dots t} + c_{3} e^{7.29589 \dots t} + 5 t - 25

y = c_{1} e^{- 0.15883 \dots t} + c_{2} e^{0.86293 \dots t} + c_{3} e^{7.29589 \dots t} + 5 t - 25