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Beliebt Rechnen >

y^{''}+4y^'+16y=0,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} + 4 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = e^{- 2 t} (cos (23 t) + \frac{1}{3} sin (23 t))

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = e^{- 2 t} (cos (23 t) + \frac{1}{3} sin (23 t))

y = e^{- 2 t} (cos (23 t) + \frac{1}{3} sin (23 t))

Graph

Beliebte Beispiele

121y^{''}+132y^'+117y=0

121 y^{^{''}} + 132 y^{^{'}} + 117 y = 0

x^{''}+4x^'+3x=0,x(0)=3

x^{^{''}} + 4 x^{^{'}} + 3 x = 0, x (0) = 3

y^{''}-8y^'-105y=0

y^{^{''}} - 8 y^{^{'}} - 105 y = 0

(d^2x)/(dt^2)+(dx)/(dt)+x=0

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 0

y^{''''}-2y^{'''}-6y^{''}=0

y^{^{''''}} - 2 y^{^{'''}} - 6 y^{^{''}} = 0