6y^{''''}+5y^{'''}+25y^{''}+20y^'+4y=0

Lösung

6 y^{^{''''}} + 5 y^{^{'''}} + 25 y^{^{''}} + 20 y^{^{'}} + 4 y = 0

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

Schritte zur Lösung

6 y^{(4)} (t) + 5 y^{'''} (t) + 25 y^{''} (t) + 20 y^{'} (t) + 4 y = 0

Solve linear ODE:

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

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

4 \frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 5 y = 0

4 y^{^{''}} + y^{^{'}} + \frac{1}{16} y = 0

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = \frac{1}{2}, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 18 y = 0

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y^{^{'}} (0) = 1, y (0) = 1