7y^{''}+3y^'+7y=0

Lösung

7 y^{^{''}} + 3 y^{^{'}} + 7 y = 0

y = e^{- \frac{3 t}{14}} (c_{1} cos (\frac{187 t}{14}) + c_{2} sin (\frac{187 t}{14}))

Schritte zur Lösung

7 y^{''} (t) + 3 y^{'} (t) + 7 y = 0

Solve linear ODE:

y = e^{- \frac{3 t}{14}} (c_{1} cos (\frac{187 t}{14}) + c_{2} sin (\frac{187 t}{14}))

y = e^{- \frac{3 t}{14}} (c_{1} cos (\frac{187 t}{14}) + c_{2} sin (\frac{187 t}{14}))

y^{^{''}} - 4 y^{^{'}} - 5 y = 0

3 y^{^{''}} - 5 y = 0

y^{^{'''}} - 6 y^{^{''}} + 5 y^{^{'}} + 12 y = 0

y^{^{''}} = 2 y^{^{'}} - y

5 y^{^{''}} - 15 y = 0