x^{''}-6x^'+8x=0

Lösung

x^{^{''}} - 6 x^{^{'}} + 8 x = 0

x = c_{1} e^{4 t} + c_{2} e^{2 t}

Schritte zur Lösung

x^{''} (t) - 6 x^{'} (t) + 8 x = 0

Solve linear ODE:

x = c_{1} e^{4 t} + c_{2} e^{2 t}

x = c_{1} e^{4 t} + c_{2} e^{2 t}

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

2 y^{^{''}} + 36 y^{^{'}} + 163 y = 0

y^{^{'''}} - 3 y^{^{''}} + 4 y^{^{'}} - 2 y = 0

3 y^{^{''}} + 7 y^{^{'}} + 2 y = 0

y^{^{''}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 3