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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 2 y = 5 e^{t} + 2 t + 2

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{'''}=3y^{''}+9e^3x+5cos(x)

y^{^{'''}} = 3 y^{^{''}} + 9 e^{3} x + 5 cos (x)

y^{''}+9y=10e^-1,y(0)=0,y^'(0)=0

y^{^{''}} + 9 y = 10 e^{-} 1, y (0) = 0, y^{^{'}} (0) = 0

y^{''}+4y^'-5y=24e^x

y^{^{''}} + 4 y^{^{'}} - 5 y = 24 e^{x}

y^{''}-4y^'+4y=e^{2x}sin(x)

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} sin (x)

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

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