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Beliebt Rechnen >

x^{''}+4x^'+5x=13sin(2t)

Lösung

x^{^{''}} + 4 x^{^{'}} + 5 x = 13 sin (2 t)

Lösung

x = e^{- 2 t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{5} sin (2 t) - \frac{8}{5} cos (2 t)

Schritte zur Lösung

x^{''} (t) + 4 x^{'} (t) + 5 x = 13 sin (2 t)

Solve linear ODE:

x = e^{- 2 t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{5} sin (2 t) - \frac{8}{5} cos (2 t)

x = e^{- 2 t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{5} sin (2 t) - \frac{8}{5} cos (2 t)

Graph

Beliebte Beispiele

y^{''}-3y^'+4y=16x-12e^{2x}

y^{^{''}} - 3 y^{^{'}} + 4 y = 16 x - 12 e^{2 x}

y^{''}-7y^'=(x-1)^2

y^{^{''}} - 7 y^{^{'}} = (x - 1)^{2}

y^{''}+y=8cos(2x)-4sin(x)

y^{^{''}} + y = 8 cos (2 x) - 4 sin (x)

y^{''}-4y=sin^2(x)

y^{^{''}} - 4 y = sin^{2} (x)

y^{''}-y=e^{2x},y(0)=1,y^'(0)=0

y^{^{''}} - y = e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0