y^{''}-6y^'+4y=0,y(0)=1,y^'(0)=1

Lösung

y^{^{''}} - 6 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 1

y = (1 - \frac{2 + 5}{2 5}) e^{(3 + 5) t} + \frac{2 + 5}{2 5} e^{(3 - 5) t}

Schritte zur Lösung

y^{''} (t) - 6 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = (1 - \frac{2 + 5}{2 5}) e^{(3 + 5) t} + \frac{2 + 5}{2 5} e^{(3 - 5) t}

y = (1 - \frac{2 + 5}{2 5}) e^{(3 + 5) t} + \frac{2 + 5}{2 5} e^{(3 - 5) t}

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

y^{^{''}} + 11 y^{^{'}} + 24 y = 0, y^{^{'}} (0) = - 7

y^{^{''}} - 18 y^{^{'}} + a y = 0, y (0) = 1, y^{^{'}} (0) = 17

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

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = 4, y^{^{'}} (0) = 0