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Beliebt Rechnen >

y^{''}+4y^'+5y=e^{-t}

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- t}

Lösung

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

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 5 y = e^{- t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+3y^'=e^x

y^{^{''}} + 3 y^{^{'}} = e^{x}

x^{^{''}} + 4 x = 4 t

y^{''}+16y=g(t),y(0)=3,y^'(0)=0

y^{^{''}} + 16 y = g (t), y (0) = 3, y^{^{'}} (0) = 0

(d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2+8x+9

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = x^{2} + 8 x + 9

y^{''}+4y^'+4y=1

y^{^{''}} + 4 y^{^{'}} + 4 y = 1