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Beliebt Rechnen >

y^{''}-4y^'-2y=2e^{-3t},y(0)=1,y^'(0)=7

Lösung

y^{^{''}} - 4 y^{^{'}} - 2 y = 2 e^{- 3 t}, y (0) = 1, y^{^{'}} (0) = 7

Lösung

y = (\frac{105 - 17 6}{38 6} + \frac{17}{19}) e^{(2 + 6) t} - \frac{105 - 17 6}{38 6} e^{(2 - 6) t} + \frac{2}{19} e^{- 3 t}

Schritte zur Lösung

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

Solve linear ODE:

y = (\frac{105 - 17 6}{38 6} + \frac{17}{19}) e^{(2 + 6) t} - \frac{105 - 17 6}{38 6} e^{(2 - 6) t} + \frac{2}{19} e^{- 3 t}

y = (\frac{105 - 17 6}{38 6} + \frac{17}{19}) e^{(2 + 6) t} - \frac{105 - 17 6}{38 6} e^{(2 - 6) t} + \frac{2}{19} e^{- 3 t}

Graph

Beliebte Beispiele

y^{''}+4y^'+12y=4x^2

y^{^{''}} + 4 y^{^{'}} + 12 y = 4 x^{2}

y^{'''}-9y^{''}+27y^'-27y=9e^{3x}

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 9 e^{3 x}

y^{''}+6y^'+5y=t*e^{-t}

y^{^{''}} + 6 y^{^{'}} + 5 y = t \cdot e^{- t}

y^{''}-6y^'-16y=-24t+32t^2

y^{^{''}} - 6 y^{^{'}} - 16 y = - 24 t + 32 t^{2}

16y^{''}+y=4sec(pi/4)

16 y^{^{''}} + y = 4 sec (\frac{π}{4})