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Beliebt Rechnen >

y^{''}+10y^'+61y=5cos(7t)

Lösung

y^{^{''}} + 10 y^{^{'}} + 61 y = 5 cos (7 t)

Lösung

y = e^{- 5 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{175}{2522} sin (7 t) + \frac{15}{1261} cos (7 t)

Schritte zur Lösung

y^{''} (t) + 10 y^{'} (t) + 61 y = 5 cos (7 t)

Solve linear ODE:

y = e^{- 5 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{175}{2522} sin (7 t) + \frac{15}{1261} cos (7 t)

y = e^{- 5 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{175}{2522} sin (7 t) + \frac{15}{1261} cos (7 t)

Graph

Beliebte Beispiele

(D^{4} - 1) y = 7 x^{2}

y^{''}-2y^'-3y=4e^{5x}

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{5 x}

y^{^{'''}} - y = 1

y^{''}+7y^'+12y=4e^{5t},y(0)=2,y^'(0)=0

y^{^{''}} + 7 y^{^{'}} + 12 y = 4 e^{5 t}, y (0) = 2, y^{^{'}} (0) = 0

y^{''}-2y^'-8y=2e^{4x}+3xe^{2x}+4x

y^{^{''}} - 2 y^{^{'}} - 8 y = 2 e^{4 x} + 3 x e^{2 x} + 4 x