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Beliebt Rechnen >

y^{''}+20y^'+500y=12

Lösung

y^{^{''}} + 20 y^{^{'}} + 500 y = 12

Lösung

y = e^{- 10 t} (c_{1} cos (20 t) + c_{2} sin (20 t)) + \frac{3}{125}

Schritte zur Lösung

y^{''} (t) + 20 y^{'} (t) + 500 y = 12

Solve linear ODE:

y = e^{- 10 t} (c_{1} cos (20 t) + c_{2} sin (20 t)) + \frac{3}{125}

y = e^{- 10 t} (c_{1} cos (20 t) + c_{2} sin (20 t)) + \frac{3}{125}

Graph

Beliebte Beispiele

limit as x approaches 2 of (x^3+7x+6)/(x^3+x^2-4x-4)

x \to 2 lim (\frac{x ^{3} + 7 x + 6}{x ^{3} + x ^{2} - 4 x - 4})

integral of 1/(2^2+3x^2)

\int \frac{1}{2 ^{2} + 3 x ^{2}} d x

f(x)=2x^3-24x^2+97x+7

f (x) = 2 x^{3} - 24 x^{2} + 97 x + 7

(d^2)/(dx^2)(x/(x-2))

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

limit as x approaches 10 of e^{-x}

x \to 10 lim (e^{- x})