y^{'''}-6y^{''}+11y^'=0

Lösung

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} = 0

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

Schritte zur Lösung

y^{'''} (t) - 6 y^{''} (t) + 11 y^{'} (t) = 0

Solve linear ODE:

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

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

81 y^{^{''}} - 234 y^{^{'}} + 169 y = 0

(d^{2} + 4 d + 4) y = 0

y^{^{'''}} - 15 y^{^{''}} + 66 y^{^{'}} - 80 y = 0

y^{^{''}} + k^{2} y^{^{'}} = 0

(d^{2} + 1)^{2} y = 0