y^{''''}=625y

Lösung

y^{^{''''}} = 625 y

y = c_{1} e^{5 t} + c_{2} e^{- 5 t} + c_{3} cos (5 t) + c_{4} sin (5 t)

Schritte zur Lösung

y^{(4)} (t) = 625 y

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 5 t} + c_{3} cos (5 t) + c_{4} sin (5 t)

y = c_{1} e^{5 t} + c_{2} e^{- 5 t} + c_{3} cos (5 t) + c_{4} sin (5 t)

y^{^{''}} + 4 y + 5 y = 0

\frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 41 y = 0

x^{^{''}} + x^{^{'}} - x = 0

\frac{d ^{3} y}{d x ^{3}} - y = 0

y^{^{''}} - 3 y^{^{'}} + y 3 = 0