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Beliebt Rechnen >

y^{''}-3y^'-4y=-8e^t(cos(2t))

Lösung

y^{^{''}} - 3 y^{^{'}} - 4 y = - 8 e^{t} (cos (2 t))

Lösung

y = c_{1} e^{4 t} + c_{2} e^{- t} + \frac{2}{13} e^{t} sin (2 t) + \frac{10}{13} e^{t} cos (2 t)

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) - 4 y = - 8 e^{t} (cos (2 t))

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- t} + \frac{2}{13} e^{t} sin (2 t) + \frac{10}{13} e^{t} cos (2 t)

y = c_{1} e^{4 t} + c_{2} e^{- t} + \frac{2}{13} e^{t} sin (2 t) + \frac{10}{13} e^{t} cos (2 t)

Graph

Beliebte Beispiele

y^{''}+y^'-12y=-32t+24t^2

y^{^{''}} + y^{^{'}} - 12 y = - 32 t + 24 t^{2}

(d^2y)/(dx^2)+y=3+e^{-x}+5e^{2x}

\frac{d ^{2} y}{d x ^{2}} + y = 3 + e^{- x} + 5 e^{2 x}

y^{''}+9y^'+14y=3sin(2x)

y^{^{''}} + 9 y^{^{'}} + 14 y = 3 sin (2 x)

x^{''}-x=e^{-t}

x^{^{''}} - x = e^{- t}

y^{''}+4y^'+4y=ln(x)

y^{^{''}} + 4 y^{^{'}} + 4 y = ln (x)