5(d^2x)/(dt^2)+3(dx)/(dt)+6x=0

Lösung

5 \frac{d ^{2} x}{d t ^{2}} + 3 \frac{d x}{d t} + 6 x = 0

x = e^{- \frac{3 t}{10}} (c_{1} cos (\frac{111 t}{10}) + c_{2} sin (\frac{111 t}{10}))

Schritte zur Lösung

5 \frac{d ^{2} x}{d t ^{2}} + 3 \frac{d x}{d t} + 6 x = 0

Solve linear ODE:

x = e^{- \frac{3 t}{10}} (c_{1} cos (\frac{111 t}{10}) + c_{2} sin (\frac{111 t}{10}))

x = e^{- \frac{3 t}{10}} (c_{1} cos (\frac{111 t}{10}) + c_{2} sin (\frac{111 t}{10}))

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 3

24 y^{^{''}} + 14 y^{^{'}} - 5 y = 0

4 y^{^{''}} + 24 y^{^{'}} + 37 y = 0, y (π) = 1, y^{^{'}} (π) = 0

y^{^{''''}} - 8 y^{^{''}} + 16 y = 0

\frac{d ^{2} x}{d t ^{2}} + 6 \frac{d x}{d t} + 3 x = 0