8(d^2y)/(dt^2)+12(dy)/(dt)+5y=0

Lösung

8 \frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 5 y = 0

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

Schritte zur Lösung

8 \frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 5 y = 0

Solve linear ODE:

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

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

\frac{d ^{2} y}{d t ^{2}} - 18 \frac{d y}{d t} + 81 y = 0

y^{^{'''}} + 4 y^{^{''}} - 25 y^{^{'}} - 28 y = 0

y^{^{''}} + 3 y^{^{'}} + 6 \cdot y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 8.1, y^{^{'}} (0) = 3.9

y^{^{'''}} + y^{^{''}} - 24 y^{^{'}} + 36 y = 0