y^{'''}-y^{''}-y^'+y=5e^{-t}+2

Lösung

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 2

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{5 e ^{- t} t}{4} + 2

Schritte zur Lösung

y^{'''} (t) - y^{''} (t) - y^{'} (t) + y = 5 e^{- t} + 2

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{5 e ^{- t} t}{4} + 2

y = c_{1} e^{- t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{5 e ^{- t} t}{4} + 2

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 4

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 6

y^{^{''}} + 7 y^{^{'}} + 6 y = 6 cos (5 t + 1.5708) H (t)

y^{^{''}} - y^{^{'}} - 2 y = sin (3 t), y (0) = 1, y (0) = - 1

y^{^{''}} + 6 y^{^{'}} + 9 y = t^{2} \cdot e^{- 3 t}