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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = - 1, y^{^{'}} (0) = 2

\frac{d ^{2} x}{d t ^{2}} - 6 \frac{d x}{d t} + 9 x = 0

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y^{^{'}} (- 1) = 9, y (- 1) = 3

y^{^{'''}} - 2 y^{^{''}} - 9 y^{^{'}} + 4 y = 0