y^{''''}+8y^{''}-4y^{'''}-16y^'+16y=0

Lösung

y^{^{''''}} + 8 y^{^{''}} - 4 y^{^{'''}} - 16 y^{^{'}} + 16 y = 0

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

Schritte zur Lösung

y^{(4)} (t) + 8 y^{''} (t) - 4 y^{'''} (t) - 16 y^{'} (t) + 16 y = 0

Solve linear ODE:

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

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

10 y^{^{''}} + 30 y^{^{'}} + 20 y = 0

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 0

\frac{d ^{4} y}{d x ^{4}} - 4 y = 0

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 5

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y^{^{'}} (0) = 2