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Beliebt Rechnen >

y^{''}+6y^'+2y=0,y(0)=4,y^'(0)=0

Lösung

y^{^{''}} + 6 y^{^{'}} + 2 y = 0, y (0) = 4, y^{^{'}} (0) = 0

Lösung

y = (4 + \frac{2 ( 3 - 7 )}{7}) e^{(- 3 + 7) t} - \frac{2 ( 3 - 7 )}{7} e^{(- 3 - 7) t}

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 2 y = 0

Solve linear ODE:

y = (4 + \frac{2 ( 3 - 7 )}{7}) e^{(- 3 + 7) t} - \frac{2 ( 3 - 7 )}{7} e^{(- 3 - 7) t}

y = (4 + \frac{2 ( 3 - 7 )}{7}) e^{(- 3 + 7) t} - \frac{2 ( 3 - 7 )}{7} e^{(- 3 - 7) t}

Graph

Beliebte Beispiele

100y^{''}-140y^'+74y=0,y(3)=6,y^'(3)=5

100 y^{^{''}} - 140 y^{^{'}} + 74 y = 0, y (3) = 6, y^{^{'}} (3) = 5

y^{''}-26y^'+233y=0

y^{^{''}} - 26 y^{^{'}} + 233 y = 0

(D^{4} + 2 D^{2}) y = 0

y^{''}+6y^'+3y=0,y(0)=0,y^'(0)=1

y^{^{''}} + 6 y^{^{'}} + 3 y = 0, y (0) = 0, y^{^{'}} (0) = 1

60x^{''}+240x=0

60 x^{^{''}} + 240 x = 0