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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{- a t} (cos (t) + a sin (t))

Schritte zur Lösung

y^{''} (t) + 2 a y^{'} (t) + (a^{2} + 1) y = 0

Solve linear ODE:

y = e^{- a t} (cos (t) + a sin (t))

y = e^{- a t} (cos (t) + a sin (t))

Graph

Beliebte Beispiele

6y^{''}-17y^'+12y=0

6 y^{^{''}} - 17 y^{^{'}} + 12 y = 0

4y^{''}+4sqrt(3)y^'+3y=0

4 y^{^{''}} + 43 y^{^{'}} + 3 y = 0

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

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

2y^{''}-y^'-3y=0,y(0)=2,y^'(0)=-7/2

2 y^{^{''}} - y^{^{'}} - 3 y = 0, y (0) = 2, y^{^{'}} (0) = - \frac{7}{2}

81y^{''}+108y^'-13y=0,y(0)=0,y^'(0)=1

81 y^{^{''}} + 108 y^{^{'}} - 13 y = 0, y (0) = 0, y^{^{'}} (0) = 1