y^{'''}+y^{''}+y^'+y=e^{-t}+13t

Lösung

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 13 t

y = c_{1} e^{- t} + c_{2} cos (t) + c_{3} sin (t) + \frac{e ^{- t} t}{2} + 13 t - 13

Schritte zur Lösung

y^{'''} (t) + y^{''} (t) + y^{'} (t) + y = e^{- t} + 13 t

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} cos (t) + c_{3} sin (t) + \frac{e ^{- t} t}{2} + 13 t - 13

y = c_{1} e^{- t} + c_{2} cos (t) + c_{3} sin (t) + \frac{e ^{- t} t}{2} + 13 t - 13

y^{^{''}} + y^{^{'}} - 6 y = - 3 sin (x) + 4 e^{2 x}

\frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} + 4 y = t e^{2 t}

y^{^{''}} - 25 y = sinh (5 x)

y^{^{''}} + y^{^{'}} - 12 y = e^{x} + e^{2 x} - 1

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = x^{2} + 2 x - 2