x^{''}+2x^'+1000x=0,x(0)=0.75,x^'(0)=0

Lösung

x^{^{''}} + 2 x^{^{'}} + 1000 x = 0, x (0) = 0.75, x^{^{'}} (0) = 0

x = e^{- t} (0.75 cos (3111 t) + 0.02372 \dots sin (3111 t))

Schritte zur Lösung

x^{''} (t) + 2 x^{'} (t) + 1000 x = 0

Solve linear ODE:

x = e^{- t} (0.75 cos (3111 t) + 0.02372 \dots sin (3111 t))

x = e^{- t} (0.75 cos (3111 t) + 0.02372 \dots sin (3111 t))

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

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

\frac{d ^{2} y}{d x ^{2}} + 9 \frac{d y}{d x} + 20 y = 0

y^{^{''}} + 12 y^{^{'}} + 27 y = 0, y (0) = 11, y^{^{'}} (0) = - 81

4 y^{^{''}} - 4 y - 3 y = 0