x^{''}+2x^'+10x=0,x(0)=1,x^'(0)=0

Lösung

x^{^{''}} + 2 x^{^{'}} + 10 x = 0, x (0) = 1, x^{^{'}} (0) = 0

x = e^{- t} (cos (3 t) + \frac{1}{3} sin (3 t))

Schritte zur Lösung

x^{''} (t) + 2 x^{'} (t) + 10 x = 0

Solve linear ODE:

x = e^{- t} (cos (3 t) + \frac{1}{3} sin (3 t))

x = e^{- t} (cos (3 t) + \frac{1}{3} sin (3 t))

\frac{16}{32} x^{^{''}} + x^{^{'}} + 2 x = 0, x (0) = - 2, x^{^{'}} (0) = 1

100 y^{^{'''}} + 60 y^{^{''}} + 9 y^{^{'}} = 0

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

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

18 y^{^{''}} + 72 y = 0, y (0) = 1, y^{^{'}} (0) = - 6