y^{''}-12y^'+27y=0

Lösung

y^{^{''}} - 12 y^{^{'}} + 27 y = 0

y = c_{1} e^{9 t} + c_{2} e^{3 t}

Schritte zur Lösung

y^{''} (t) - 12 y^{'} (t) + 27 y = 0

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} e^{3 t}

y = c_{1} e^{9 t} + c_{2} e^{3 t}

y^{^{'''}} - 4 y^{^{''}} + 8 y^{^{'}} = 0

6 y^{^{''}} + 11 y^{^{'}} - 6 y = 0

(D^{2} - D - 6) y = 0

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

x^{^{''}} + 5 x^{^{'}} + 4 x = 0