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Beliebt Rechnen >

y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = (1 + \frac{1}{3}) e^{- 2 t} - \frac{1}{3} e^{- 8 t}

Schritte zur Lösung

y^{''} (t) + 10 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = (1 + \frac{1}{3}) e^{- 2 t} - \frac{1}{3} e^{- 8 t}

y = (1 + \frac{1}{3}) e^{- 2 t} - \frac{1}{3} e^{- 8 t}

Graph

Beliebte Beispiele

y^{''}+4000y^'+4000000y=0

y^{^{''}} + 4000 y^{^{'}} + 4000000 y = 0

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

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

x^{''}+x^'+1/3 x=0,x(0)=4,x^'(0)=0

x^{^{''}} + x^{^{'}} + \frac{1}{3} x = 0, x (0) = 4, x^{^{'}} (0) = 0

y^{'''}+3y^{''}-10y^'=0

y^{^{'''}} + 3 y^{^{''}} - 10 y^{^{'}} = 0

81y^{''}-18y^'+5y=0,y(1)=1,y^'(1)=7

81 y^{^{''}} - 18 y^{^{'}} + 5 y = 0, y (1) = 1, y^{^{'}} (1) = 7