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Beliebt Rechnen >

1/4 x^{''}+10x^'+1000x=0

Lösung

\frac{1}{4} x^{^{''}} + 10 x^{^{'}} + 1000 x = 0

Lösung

x = e^{- 20 t} (c_{1} cos (60 t) + c_{2} sin (60 t))

Schritte zur Lösung

\frac{1}{4} x^{''} (t) + 10 x^{'} (t) + 1000 x = 0

Solve linear ODE:

x = e^{- 20 t} (c_{1} cos (60 t) + c_{2} sin (60 t))

x = e^{- 20 t} (c_{1} cos (60 t) + c_{2} sin (60 t))

Graph

Beliebte Beispiele

4y^{'''}-7y^{''}-34y^'-8y=0

4 y^{^{'''}} - 7 y^{^{''}} - 34 y^{^{'}} - 8 y = 0

y^{''}-6y^'+13y=0,y(0)=1,y^'(0)=5

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = 5

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

l in e a r 4 y^{^{''}} - y = 0, y (0) = 0, y^{^{'}} (0) = 1

(4D^5-15D^3-5D^2+15D+9)y=0

(4 D^{5} - 15 D^{3} - 5 D^{2} + 15 D + 9) y = 0

f^{''}(x)=6f^'(x)-6f(x)

f^{^{''}} (x) = 6 f^{^{'}} (x) - 6 f (x)