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Beliebt Rechnen >

x^{''}+2x^'+41x=11cos(6t)

Lösung

x^{^{''}} + 2 x^{^{'}} + 41 x = 11 cos (6 t)

Lösung

x = e^{- t} (c_{1} cos (210 t) + c_{2} sin (210 t)) + \frac{132}{169} sin (6 t) + \frac{55}{169} cos (6 t)

Schritte zur Lösung

x^{''} (t) + 2 x^{'} (t) + 41 x = 11 cos (6 t)

Solve linear ODE:

x = e^{- t} (c_{1} cos (210 t) + c_{2} sin (210 t)) + \frac{132}{169} sin (6 t) + \frac{55}{169} cos (6 t)

x = e^{- t} (c_{1} cos (210 t) + c_{2} sin (210 t)) + \frac{132}{169} sin (6 t) + \frac{55}{169} cos (6 t)

Graph

Beliebte Beispiele

y^{''}+y^'=sin(x)+cos(x)

y^{^{''}} + y^{^{'}} = sin (x) + cos (x)

y^{'''}+y^{''}+4y^'+4y=4x+4

y^{^{'''}} + y^{^{''}} + 4 y^{^{'}} + 4 y = 4 x + 4

y^{''}-3y^'+2y=4e^{2t},y^'(0)=5,y(0)=-3

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{2 t}, y^{^{'}} (0) = 5, y (0) = - 3

y^{''}-4y^'+8y=16x

y^{^{''}} - 4 y^{^{'}} + 8 y = 16 x

(d^{2} + 1) y = x^{3}