x^{''}-6x=0

Lösung

x^{^{''}} - 6 x = 0

x = c_{1} e^{6 t} + c_{2} e^{- 6 t}

Schritte zur Lösung

x^{''} (t) - 6 x = 0

Solve linear ODE:

x = c_{1} e^{6 t} + c_{2} e^{- 6 t}

x = c_{1} e^{6 t} + c_{2} e^{- 6 t}

y^{^{''}} + y^{^{'}} - \frac{10}{3} y = 0

x^{^{''}} + 8 x^{^{'}} + 4 x = 0

\frac{d ^{3} y}{d x ^{3}} + \frac{d y}{d x} = 0

4 y + 9 y^{^{''}} = - 12 y^{^{'}}

9 y^{^{''}} + 12 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 0