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Beliebt Rechnen >

y^{''}+2y^'+5y=9sin(2t)

Lösung

y^{^{''}} + 2 y^{^{'}} + 5 y = 9 sin (2 t)

Lösung

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{9}{17} sin (2 t) - \frac{36}{17} cos (2 t)

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 5 y = 9 sin (2 t)

Solve linear ODE:

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{9}{17} sin (2 t) - \frac{36}{17} cos (2 t)

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{9}{17} sin (2 t) - \frac{36}{17} cos (2 t)

Graph

Beliebte Beispiele

integral of ln|x+1|

\int ln ∣ x + 1 ∣ d x

derivative of (x^2-3x^5)

\frac{d}{d x} ((x^{2} - 3 x)^{5})

(12x^2+y-1)dx-(6y-x)dy=0,y(1)=0

(12 x^{2} + y - 1) d x - (6 y - x) d y = 0, y (1) = 0

derivative of e^{2x+3y}

\frac{d}{d x} (e^{2 x + 3 y})

implicit (dy)/(dx),y=5^x

im pl i c i t \frac{d y}{d x}, y = 5^{x}