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

Lösung

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

y = e^{2 t} (a + \frac{2 - 2 a}{3}) - \frac{e ^{- t} ( 2 - 2 a )}{3}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{2 t} (a + \frac{2 - 2 a}{3}) - \frac{e ^{- t} ( 2 - 2 a )}{3}

y = e^{2 t} (a + \frac{2 - 2 a}{3}) - \frac{e ^{- t} ( 2 - 2 a )}{3}

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 0

2 y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} - 20 y = 0, y (0) = 1, y (0) = 22

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

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