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Beliebt Rechnen >

x^{''}+4x^'+20x=4cos(2t)

Lösung

x^{^{''}} + 4 x^{^{'}} + 20 x = 4 cos (2 t)

Lösung

x = e^{- 2 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + \frac{1}{10} sin (2 t) + \frac{1}{5} cos (2 t)

Schritte zur Lösung

x^{''} (t) + 4 x^{'} (t) + 20 x = 4 cos (2 t)

Solve linear ODE:

x = e^{- 2 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + \frac{1}{10} sin (2 t) + \frac{1}{5} cos (2 t)

x = e^{- 2 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + \frac{1}{10} sin (2 t) + \frac{1}{5} cos (2 t)

Graph

Beliebte Beispiele

y^{''}+y^'-6y=-5e^{-2x}

y^{^{''}} + y^{^{'}} - 6 y = - 5 e^{- 2 x}

y^{''}+y=3cos(4t),y(0)=1,y^'(0)=2

y^{^{''}} + y = 3 cos (4 t), y (0) = 1, y^{^{'}} (0) = 2

x^{''}+x= 1/(cos(t))

x^{^{''}} + x = \frac{1}{cos ( t )}

y^{''}-6y^'+10y=e^{3x}cos(x)

y^{^{''}} - 6 y^{^{'}} + 10 y = e^{3 x} cos (x)

y^{''}+y=x^2+sin(x)

y^{^{''}} + y = x^{2} + sin (x)