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Beliebt Rechnen >

25x^{''}+5x^'+204.167x=0,x(0)=28.577

Lösung

25 x^{^{''}} + 5 x^{^{'}} + 204.167 x = 0, x (0) = 28.577

Lösung

x = e^{- \frac{t}{10}} (28.577 cos (\frac{20391700000 t}{50000}) + c_{2} sin (\frac{20391700000 t}{50000}))

Schritte zur Lösung

25 x^{''} (t) + 5 x^{'} (t) + 204.167 x = 0

Solve linear ODE:

x = e^{- \frac{t}{10}} (28.577 cos (\frac{20391700000 t}{50000}) + c_{2} sin (\frac{20391700000 t}{50000}))

x = e^{- \frac{t}{10}} (28.577 cos (\frac{20391700000 t}{50000}) + c_{2} sin (\frac{20391700000 t}{50000}))

Graph

Beliebte Beispiele

y^{''}+2y^'+5y=0,y(0)=2,y^'(0)=4

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 4

(d^2y)/(dt^2)-14(dy)/(dt)+149y=0

\frac{d ^{2} y}{d t ^{2}} - 14 \frac{d y}{d t} + 149 y = 0

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

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

1/8 y^{''}+16y=0

\frac{1}{8} y^{^{''}} + 16 y = 0

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