x^{''}-2x^'-x=0

Lösung

x^{^{''}} - 2 x^{^{'}} - x = 0

x = c_{1} e^{(1 + 2) t} + c_{2} e^{(1 - 2) t}

Schritte zur Lösung

x^{''} (t) - 2 x^{'} (t) - x = 0

Solve linear ODE:

x = c_{1} e^{(1 + 2) t} + c_{2} e^{(1 - 2) t}

x = c_{1} e^{(1 + 2) t} + c_{2} e^{(1 - 2) t}

y^{^{'''}} + 3 y^{^{''}} - 28 y^{^{'}} = 0

y^{^{''}} + 4 y = 0, y (0) = 3, y^{^{'}} (0) = 8

x^{^{''}} + 3 x^{^{'}} = 2 x - (x^{^{'}} + 3 x)

y^{^{''}} + 2 \cdot y = 0

25 y^{^{''}} - 90 y^{^{'}} + 81 y = 0