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Beliebt Rechnen >

1/8 y^{''}+4y^'+16y=0,y(0)=0,y^'(0)=9

Lösung

\frac{1}{8} y^{^{''}} + 4 y^{^{'}} + 16 y = 0, y (0) = 0, y^{^{'}} (0) = 9

Lösung

y = \frac{9}{16 2} e^{8 (2 - 2) t} - \frac{9}{16 2} e^{- 8 (2 + 2) t}

Schritte zur Lösung

\frac{1}{8} y^{''} (t) + 4 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = \frac{9}{16 2} e^{8 (2 - 2) t} - \frac{9}{16 2} e^{- 8 (2 + 2) t}

y = \frac{9}{16 2} e^{8 (2 - 2) t} - \frac{9}{16 2} e^{- 8 (2 + 2) t}

Graph

Beliebte Beispiele

2y^{'''}-y^{''}-y=0

2 y^{^{'''}} - y^{^{''}} - y = 0

y^{''}-y=0,y(0)=e^x

y^{^{''}} - y = 0, y (0) = e^{x}

y^{''}-10y^'+25y=0,y(0)=e^{5x}

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = e^{5 x}

-4y^{''}+y^'=0,y(0)=1,y(1)=0

- 4 y^{^{''}} + y^{^{'}} = 0, y (0) = 1, y (1) = 0

(d^2y)/(dx^2)+7(dy)/(dx)+10y=0

\frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} + 10 y = 0