3y^{'''}+11y^{''}+24y^'+12y=0

Lösung

3 y^{^{'''}} + 11 y^{^{''}} + 24 y^{^{'}} + 12 y = 0

y = c_{1} e^{- \frac{2 t}{3}} + e^{- \frac{3 t}{2}} (c_{2} cos (\frac{15 t}{2}) + c_{3} sin (\frac{15 t}{2}))

Schritte zur Lösung

3 y^{'''} (t) + 11 y^{''} (t) + 24 y^{'} (t) + 12 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{2 t}{3}} + e^{- \frac{3 t}{2}} (c_{2} cos (\frac{15 t}{2}) + c_{3} sin (\frac{15 t}{2}))

y = c_{1} e^{- \frac{2 t}{3}} + e^{- \frac{3 t}{2}} (c_{2} cos (\frac{15 t}{2}) + c_{3} sin (\frac{15 t}{2}))

(D^{2} + 2 D + 17) y = 0

3 y^{^{'''}} - 5 y^{^{''}} - 16 y^{^{'}} + 12 y = 0

y^{^{''}} + y^{^{'}} + 4.25 y = 0, y (0) = 5

y^{^{''}} + 0 y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = 0

y^{^{''}} - 12 y^{^{'}} + 40 y = 0, y (0) = 6, y^{^{'}} (0) = - 2