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Beliebt Rechnen >

y^{''}+6y^'+25y=15cos(5t)

Lösung

y^{^{''}} + 6 y^{^{'}} + 25 y = 15 cos (5 t)

Lösung

y = e^{- 3 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + \frac{1}{2} sin (5 t)

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 25 y = 15 cos (5 t)

Solve linear ODE:

y = e^{- 3 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + \frac{1}{2} sin (5 t)

y = e^{- 3 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + \frac{1}{2} sin (5 t)

Graph

Beliebte Beispiele

y^{''}-4y^'+4y=2t^6e^{2t}

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 t^{6} e^{2 t}

y^{''}-2y^'+y=t^{-7}e^t

y^{^{''}} - 2 y^{^{'}} + y = t^{- 7} e^{t}

y^{''}-y-2=0,y(0)=3

y^{^{''}} - y - 2 = 0, y (0) = 3

y^{''}-6y^'+8y=2

y^{^{''}} - 6 y^{^{'}} + 8 y = 2

y^{''}+3y^'-4=0

y^{^{''}} + 3 y^{^{'}} - 4 = 0