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Beliebt Rechnen >

(d^2y)/(dx^2)+4(dy)/(dx)+8y=8e^{-2x}

Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 8 y = 8 e^{- 2 x}

Lösung

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

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 8 y = 8 e^{- 2 x}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

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

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

y^{''}-y^'-12y=98(x+2)e^{-3x}

y^{^{''}} - y^{^{'}} - 12 y = 98 (x + 2) e^{- 3 x}

y^{''}+2y^'+y=(1/6)e^{-x}

y^{^{''}} + 2 y^{^{'}} + y = (\frac{1}{6}) e^{- x}

y^{'''}+2y^{''}-y^'-2y=5\H(t)

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

y^{''''}+3y^{'''}-4y^{''}-4y^'+1/2 =0

y^{^{''''}} + 3 y^{^{'''}} - 4 y^{^{''}} - 4 y^{^{'}} + \frac{1}{2} = 0