f^{''}(t)-f^'(t)-2f(t)=0,f(0)=1,f^'(0)=0

Lösung

f^{^{''}} (t) - f^{^{'}} (t) - 2 f (t) = 0, f (0) = 1, f^{^{'}} (0) = 0

f (t) = (1 - \frac{2}{3}) e^{2 t} + \frac{2}{3} e^{- t}

Schritte zur Lösung

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

Solve linear ODE:

f (t) = (1 - \frac{2}{3}) e^{2 t} + \frac{2}{3} e^{- t}

f (t) = (1 - \frac{2}{3}) e^{2 t} + \frac{2}{3} e^{- t}

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 29 y = 0

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 4000 y^{^{'}} + 4000000 y = 0

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