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

Lösung

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

y = c_{1} e^{- t} + c_{2} cos (t) + c_{3} sin (t) + \frac{e ^{- t} t}{2} + 7 t - 7

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} cos (t) + c_{3} sin (t) + \frac{e ^{- t} t}{2} + 7 t - 7

y = c_{1} e^{- t} + c_{2} cos (t) + c_{3} sin (t) + \frac{e ^{- t} t}{2} + 7 t - 7

y^{^{''}} - 2 y^{^{'}} + y = 6 t - 2, y (- 1) = 3, y^{^{'}} (- 1) = 7

y^{^{''}} + 4 y^{^{'}} + y = 4, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2 x} (sin (x) + 2 cos (x))

y^{^{''}} - 3 y^{^{'}} + 5 y = 24 e^{- 2 x}

x^{^{''}} + 5 x^{^{'}} + 6 x = 2 e^{- t}