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

Lösung

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

y = c_{1} e^{\frac{4 t}{7}} + c_{2} e^{- \frac{4 t}{7}}

Schritte zur Lösung

y^{''} (t) - 8 y^{''} (t) + 16 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{4 t}{7}} + c_{2} e^{- \frac{4 t}{7}}

y = c_{1} e^{\frac{4 t}{7}} + c_{2} e^{- \frac{4 t}{7}}

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

y^{^{''}} - 2 y^{^{'}} + 13 y = 0

y^{^{''}} + 9 y^{^{'}} + 17 y = 0

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = - 3, y^{^{'}} (0) = - 4