y^{'''}-2y^{''}+8y^'=0

Lösung

y^{^{'''}} - 2 y^{^{''}} + 8 y^{^{'}} = 0

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

Schritte zur Lösung

y^{'''} (t) - 2 y^{''} (t) + 8 y^{'} (t) = 0

Solve linear ODE:

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

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

5 y^{^{''}} + 25 y = 0

- x^{^{''}} + 2 x^{^{'}} + x = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 3, y^{^{'}} (0) = 1

(D^{2} - 1) y = 0

9 y^{^{''}} - 5 y^{^{'}} - 4 y = 0