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Beliebt Rechnen >

y^{''}+12y^'+27y=0,y(0)=11,y^'(0)=-81

Lösung

y^{^{''}} + 12 y^{^{'}} + 27 y = 0, y (0) = 11, y^{^{'}} (0) = - 81

Lösung

y = 3 e^{- 3 t} + 8 e^{- 9 t}

Schritte zur Lösung

y^{''} (t) + 12 y^{'} (t) + 27 y = 0

Solve linear ODE:

y = 3 e^{- 3 t} + 8 e^{- 9 t}

y = 3 e^{- 3 t} + 8 e^{- 9 t}

Graph

Beliebte Beispiele

4y^{''}-4y-3y=0

4 y^{^{''}} - 4 y - 3 y = 0

(d^2x)/(dt^2)+10(dx)/(dt)+25x=0

\frac{d ^{2} x}{d t ^{2}} + 10 \frac{d x}{d t} + 25 x = 0

y^{''}+10y^'+16y=0,y(0)=9,y^'(0)=-60

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 9, y^{^{'}} (0) = - 60

y^{'''}-7y^{''}+12y^'=0

y^{^{'''}} - 7 y^{^{''}} + 12 y^{^{'}} = 0

(d^2x)/(dt^2)-4(dx)/(dt)+5x=0

\frac{d ^{2} x}{d t ^{2}} - 4 \frac{d x}{d t} + 5 x = 0