y^{'''}-6y^{''}+9y^'=0

Lösung

y^{^{'''}} - 6 y^{^{''}} + 9 y^{^{'}} = 0

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

Schritte zur Lösung

y^{'''} (t) - 6 y^{''} (t) + 9 y^{'} (t) = 0

Solve linear ODE:

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

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

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

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 2 y = 0

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

y^{^{''}} - 9 y^{^{'}} + 14 y = 0

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