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Beliebt Rechnen >

x^{''}+2x^'+5x=sin(2t)

Lösung

x^{^{''}} + 2 x^{^{'}} + 5 x = sin (2 t)

Lösung

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{17} sin (2 t) - \frac{4}{17} cos (2 t)

Schritte zur Lösung

x^{''} (t) + 2 x^{'} (t) + 5 x = sin (2 t)

Solve linear ODE:

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{17} sin (2 t) - \frac{4}{17} cos (2 t)

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{17} sin (2 t) - \frac{4}{17} cos (2 t)

Graph

Beliebte Beispiele

y^{''}-y^'-2y=3e^{-x}

y^{^{''}} - y^{^{'}} - 2 y = 3 e^{- x}

y^{''}+3y^'+2y=12e^t

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 e^{t}

y^{''}-2y^'-3y=3t^2

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t^{2}

(D^2-2D+3)y=x^3+sin(x)

(D^{2} - 2 D + 3) y = x^{3} + sin (x)

y^{''}+y=16cos(t),y(0)=0,y^'(0)=0

y^{^{''}} + y = 16 cos (t), y (0) = 0, y^{^{'}} (0) = 0