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Beliebt Rechnen >

y^{''}+y^'+5y=4e^{-t}cos(2t)

Lösung

y^{^{''}} + y^{^{'}} + 5 y = 4 e^{- t} cos (2 t)

Lösung

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{19 t}{2}) + c_{2} sin (\frac{19 t}{2})) - \frac{8}{5} e^{- t} sin (2 t) + \frac{4}{5} e^{- t} cos (2 t)

Schritte zur Lösung

y^{''} (t) + y^{'} (t) + 5 y = 4 e^{- t} cos (2 t)

Solve linear ODE:

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{19 t}{2}) + c_{2} sin (\frac{19 t}{2})) - \frac{8}{5} e^{- t} sin (2 t) + \frac{4}{5} e^{- t} cos (2 t)

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{19 t}{2}) + c_{2} sin (\frac{19 t}{2})) - \frac{8}{5} e^{- t} sin (2 t) + \frac{4}{5} e^{- t} cos (2 t)

Graph

Beliebte Beispiele

y^{''}-5y^'+4y=e^{2t}

y^{^{''}} - 5 y^{^{'}} + 4 y = e^{2 t}

y^{''}-6y^'+8y=4e^{4x}

y^{^{''}} - 6 y^{^{'}} + 8 y = 4 e^{4 x}

y^{'''}-y^{''}=6

y^{^{'''}} - y^{^{''}} = 6

y^{''}+2y^'-3y=t,y(0)=2,y^'(0)=1

y^{^{''}} + 2 y^{^{'}} - 3 y = t, y (0) = 2, y^{^{'}} (0) = 1

y^{''}+4y=3sin(x)+3cos(x)

y^{^{''}} + 4 y = 3 sin (x) + 3 cos (x)