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

Lösung

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

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

Schritte zur Lösung

2 y^{'''} (t) - 4 y^{''} (t) - 2 y^{'} (t) + 4 y = 0

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 5 y = 0

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

y^{^{''}} - y^{^{'}} - 56 y = 0, y (0) = - 5, y^{^{'}} (0) = 5

y^{^{''}} + 36 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{24}{5}

y^{^{''}} + 2 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = - 3