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Beliebt Rechnen >

y^{''}+8y^'+20y=0,y(0)=2,y^'(0)=-7

Lösung

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

Lösung

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

Schritte zur Lösung

y^{''} (t) + 8 y^{'} (t) + 20 y = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

(d^2y)/(dx^2)-5y=0

\frac{d ^{2} y}{d x ^{2}} - 5 y = 0

2y^{''}+8y^'+80y=0

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 0

y^{''}+6y^'+9y=0,y(0)=2,y^'(0)=3

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 3

y^{''}-6y^'+14y=0

y^{^{''}} - 6 y^{^{'}} + 14 y = 0

x^{^{''}} + a^{2} x = 0