y^{'''}+5y^{''}-16y^'-170y=0

Lösung

y^{^{'''}} + 5 y^{^{''}} - 16 y^{^{'}} - 170 y = 0

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

Schritte zur Lösung

y^{'''} (t) + 5 y^{''} (t) - 16 y^{'} (t) - 170 y = 0

Solve linear ODE:

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

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

y^{^{''}} - 35 y = 0

y^{^{''''}} - 4 y^{^{'''}} - 16 y^{^{''}} + 64 y^{^{'}} = 0

5 y^{^{''}} - 7 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = - 0.8

4 x^{^{''}} + x^{^{'}} + 2 x = 0, x (0) = 0, x (0) = - 1, x^{^{'}} (0) = 12

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