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

Lösung

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

y = c_{1} + c_{2} e^{3 t} + c_{3} e^{- 4 t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{3 t} + c_{3} e^{- 4 t}

y = c_{1} + c_{2} e^{3 t} + c_{3} e^{- 4 t}

8 y^{^{''}} + 23 y^{^{'}} - 3 y = 0

4 y^{^{''}} + 11 y^{^{'}} - 3 y = 0

y^{^{'''}} = 2 y^{^{'}}

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

64 y^{^{'''}} + 112 y^{^{''}} + 49 y^{^{'}} = 0