(d^2x)/(dt^2)+2a(dx)/(dt)+b^2x=0,a<b

Lösung

\frac{d ^{2} x}{d t ^{2}} + 2 a \frac{d x}{d t} + b^{2} x = 0, a < b

x = c_{1} e^{(- a + a^{2} - b^{2}) t} + c_{2} e^{(- a - a^{2} - b^{2}) t}

Schritte zur Lösung

\frac{d ^{2} x}{d t ^{2}} + 2 a \frac{d x}{d t} + b^{2} x = 0

Solve linear ODE:

x = c_{1} e^{(- a + a^{2} - b^{2}) t} + c_{2} e^{(- a - a^{2} - b^{2}) t}

x = c_{1} e^{(- a + a^{2} - b^{2}) t} + c_{2} e^{(- a - a^{2} - b^{2}) t}

x^{^{''}} + 4 x^{^{'}} + 5 x = 0, x (0) = 0, x^{^{'}} (0) = 4

y^{^{''}} + 81 y = 0, y (0) = 3, y^{^{'}} (0) = 8

14 y^{^{''}} - 15 y^{^{'}} + y = 0, y (0) = 14, y^{^{'}} (0) = \frac{1}{14}

5 y^{^{''}} - 7 y^{^{'}} - 3 y = 0

y^{^{''}} - 6 y^{^{'}} + 18 y = 0, y (0) = 0, y^{^{'}} (0) = 6