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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + 2 y = e^{- t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

(D^2-3D+2)y=2x^3-9x^2+6x

(D^{2} - 3 D + 2) y = 2 x^{3} - 9 x^{2} + 6 x

y^{''}+6y^'+13y=7cos(3t+pi/4)

y^{^{''}} + 6 y^{^{'}} + 13 y = 7 cos (3 t + \frac{π}{4})

y^{''}+2y^'-8y=e^{2t}+5t

y^{^{''}} + 2 y^{^{'}} - 8 y = e^{2 t} + 5 t

y^{''}+2y^'+2y=e^{{-2x}}cos(x)

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{{- 2 x}} cos (x)

y^{''}-y^'-2y=2e^x

y^{^{''}} - y^{^{'}} - 2 y = 2 e^{x}