y^{'''}-8y^{''}+37y^'-50y=0

Lösung

y^{^{'''}} - 8 y^{^{''}} + 37 y^{^{'}} - 50 y = 0

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

Schritte zur Lösung

y^{'''} (t) - 8 y^{''} (t) + 37 y^{'} (t) - 50 y = 0

Solve linear ODE:

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

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

(d^{3} - 9 d) \cdot y = 0

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

(d^{4} - 7 d^{3} + 18 d^{2} - 20 d + 8) y = 0

(d^{3} - d^{2}) y = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 3