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

Lösung

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

y = (1 + \frac{3 - 2 2}{4 2}) e^{2 (1 + 2) t} - \frac{3 - 2 2}{4 2} e^{2 (1 - 2) t}

Schritte zur Lösung

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

Solve linear ODE:

y = (1 + \frac{3 - 2 2}{4 2}) e^{2 (1 + 2) t} - \frac{3 - 2 2}{4 2} e^{2 (1 - 2) t}

y = (1 + \frac{3 - 2 2}{4 2}) e^{2 (1 + 2) t} - \frac{3 - 2 2}{4 2} e^{2 (1 - 2) t}

y^{^{''}} - 4 y^{^{'}} - 4 y = 0, y (0) = 2, y^{^{'}} (0) = 16

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 3, y (0) = - 12

(D^{5} - 6 D^{4} + 9 D^{3}) y = 0

y^{^{''}} + 4 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0

121 y^{^{''}} + 132 y^{^{'}} + 117 y = 0