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Beliebt Rechnen >

0.5y^{''}+6y^'+50y=0

Lösung

0.5 y^{^{''}} + 6 y^{^{'}} + 50 y = 0

Lösung

y = e^{- 6 t} (c_{1} cos (8 t) + c_{2} sin (8 t))

Schritte zur Lösung

0.5 y^{''} (t) + 6 y^{'} (t) + 50 y = 0

Solve linear ODE:

y = e^{- 6 t} (c_{1} cos (8 t) + c_{2} sin (8 t))

y = e^{- 6 t} (c_{1} cos (8 t) + c_{2} sin (8 t))

Graph

Beliebte Beispiele

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

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

(d^3y)/(dx^3)=(dy)/(dx)

\frac{d ^{3} y}{d x ^{3}} = \frac{d y}{d x}

16y^{''''}=625y

16 y^{^{''''}} = 625 y

y^{''}+64y=0,y(0)= 2/3 ,y^'(0)=-4/3

y^{^{''}} + 64 y = 0, y (0) = \frac{2}{3}, y^{^{'}} (0) = - \frac{4}{3}

(4D^3+4D^2+D)y=0

(4 D^{3} + 4 D^{2} + D) y = 0