y^{''''}+8y^{''}+16y=48+cos(4t)

Lösung

y^{^{''''}} + 8 y^{^{''}} + 16 y = 48 + cos (4 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) + t (c_{3} cos (2 t) + c_{4} sin (2 t)) + 3 + \frac{1}{144} cos (4 t)

Schritte zur Lösung

y^{(4)} (t) + 8 y^{''} (t) + 16 y = 48 + cos (4 t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + t (c_{3} cos (2 t) + c_{4} sin (2 t)) + 3 + \frac{1}{144} cos (4 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) + t (c_{3} cos (2 t) + c_{4} sin (2 t)) + 3 + \frac{1}{144} cos (4 t)

y^{^{''}} + 16 y = 32 t

y^{^{''}} + 2 y^{^{'}} + 5 y = 24 e^{- t} cos (2 t)

y^{^{''}} - 5 y^{^{'}} + 4 y = \frac{6}{1 + e ^{- 2 x}}

y^{^{''}} + y = c

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 8 e^{4 x}