y^{''}+3y^'-10y=0,y(0)=1,y^'(0)=9

Lösung

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = 9

y = 2 e^{2 t} - e^{- 5 t}

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) - 10 y = 0

Solve linear ODE:

y = 2 e^{2 t} - e^{- 5 t}

y = 2 e^{2 t} - e^{- 5 t}

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

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

(D^{2} - 3 D - 10) y = 0

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

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 6, y^{^{'}} (- 1) = 5