10x^{''}+7x^'+x=0

Lösung

10 x^{^{''}} + 7 x^{^{'}} + x = 0

x = c_{1} e^{- \frac{t}{5}} + c_{2} e^{- \frac{t}{2}}

Schritte zur Lösung

10 x^{''} (t) + 7 x^{'} (t) + x = 0

Solve linear ODE:

x = c_{1} e^{- \frac{t}{5}} + c_{2} e^{- \frac{t}{2}}

x = c_{1} e^{- \frac{t}{5}} + c_{2} e^{- \frac{t}{2}}

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (- 1) = 3, y^{^{'}} (- 1) = 5

4 y^{^{''}} - y^{^{'}} - 6 y = 0

y^{^{''}} - \frac{2}{3} y^{^{'}} + \frac{y}{9} = 0, y (0) = 17, y^{^{'}} (0) = b

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 1, y^{^{'}} (0) = 7

y^{^{''}} + 10 y + 16 y = 0