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Beliebt Rechnen >

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

Lösung

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

Lösung

x = e^{- \frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + \frac{1}{2} sin (t) - \frac{1}{2} cos (t)

Schritte zur Lösung

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

Solve linear ODE:

x = e^{- \frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + \frac{1}{2} sin (t) - \frac{1}{2} cos (t)

x = e^{- \frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + \frac{1}{2} sin (t) - \frac{1}{2} cos (t)

Graph

Beliebte Beispiele

q^{''}+10q^'+10000q=20(t)

q^{^{''}} + 10 q^{^{'}} + 10000 q = 20 (t)

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

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

y^{''}+y^'-2y=2+5*cos(x)

y^{^{''}} + y^{^{'}} - 2 y = 2 + 5 \cdot cos (x)

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

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

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

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