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Beliebt Rechnen >

y^{''}+4y^'+13y=0,y(0)=4,y^'(0)=-7

Lösung

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 4, y^{^{'}} (0) = - 7

Lösung

y = e^{- 2 t} (4 cos (3 t) + \frac{1}{3} sin (3 t))

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 13 y = 0

Solve linear ODE:

y = e^{- 2 t} (4 cos (3 t) + \frac{1}{3} sin (3 t))

y = e^{- 2 t} (4 cos (3 t) + \frac{1}{3} sin (3 t))

Graph

Beliebte Beispiele

y^{''}-2y^'+y=0,y(2)=1,y^'(2)=2

y^{^{''}} - 2 y^{^{'}} + y = 0, y (2) = 1, y^{^{'}} (2) = 2

y^{''}+14y^'+51y=0

y^{^{''}} + 14 y^{^{'}} + 51 y = 0

y^{'''}-4y^{''}-5y^'=0,y(1)=0,y^'(1)=8

y^{^{'''}} - 4 y^{^{''}} - 5 y^{^{'}} = 0, y (1) = 0, y^{^{'}} (1) = 8

y^{''}-1y^'+0.1y=0

y^{^{''}} - 1 y^{^{'}} + 0.1 y = 0

(d^{4} - 1) y = 0