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Beliebt Rechnen >

y^{''}+40y^'+400y=100sin(10t)

Lösung

y^{^{''}} + 40 y^{^{'}} + 400 y = 100 sin (10 t)

Lösung

y = c_{1} e^{- 20 t} + c_{2} t e^{- 20 t} + \frac{3}{25} sin (10 t) - \frac{4}{25} cos (10 t)

Schritte zur Lösung

y^{''} (t) + 40 y^{'} (t) + 400 y = 100 sin (10 t)

Solve linear ODE:

y = c_{1} e^{- 20 t} + c_{2} t e^{- 20 t} + \frac{3}{25} sin (10 t) - \frac{4}{25} cos (10 t)

y = c_{1} e^{- 20 t} + c_{2} t e^{- 20 t} + \frac{3}{25} sin (10 t) - \frac{4}{25} cos (10 t)

Graph

Beliebte Beispiele

y^{^{''}} + 7 y = x

y^{''}-y^'-6y=14cos(3x)

y^{^{''}} - y^{^{'}} - 6 y = 14 cos (3 x)

y^{''}+4000y^'+4000000y=36

y^{^{''}} + 4000 y^{^{'}} + 4000000 y = 36

(d^2y)/(dx^2)+14(dy)/(dx)+49y=4e^{5x}

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 49 y = 4 e^{5 x}

y^{^{''}} + 3 y + 2 = 0