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Beliebt Rechnen >

y^{''}-y^'-2y=e^{-2t}-3e^{-t}

Lösung

y^{^{''}} - y^{^{'}} - 2 y = e^{- 2 t} - 3 e^{- t}

Lösung

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{4} e^{- 2 t} + e^{- t} t

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 2 y = e^{- 2 t} - 3 e^{- t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{4} e^{- 2 t} + e^{- t} t

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{4} e^{- 2 t} + e^{- t} t

Graph

Beliebte Beispiele

y^{''}-2y^'+2y-3cos(x)=e^x

y^{^{''}} - 2 y^{^{'}} + 2 y - 3 cos (x) = e^{x}

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

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

x^{''}+3x^'+61/4 x= 1/2 e^t

x^{^{''}} + 3 x^{^{'}} + \frac{61}{4} x = \frac{1}{2} e^{t}

y^{''}+4y^'=3sin(2t)

y^{^{''}} + 4 y^{^{'}} = 3 sin (2 t)

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

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