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Beliebt Rechnen >

9y^{''}+4y^'+5y=0,y(0)=2,y^'(0)=0

Lösung

9 y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 0

Lösung

y = e^{- \frac{2 t}{9}} (2 cos (\frac{41 t}{9}) + \frac{4}{41} sin (\frac{41 t}{9}))

Schritte zur Lösung

9 y^{''} (t) + 4 y^{'} (t) + 5 y = 0

Solve linear ODE:

y = e^{- \frac{2 t}{9}} (2 cos (\frac{41 t}{9}) + \frac{4}{41} sin (\frac{41 t}{9}))

y = e^{- \frac{2 t}{9}} (2 cos (\frac{41 t}{9}) + \frac{4}{41} sin (\frac{41 t}{9}))

Graph

Beliebte Beispiele

4 y^{^{''}} - 36 y = 0

100y^{''}+60y^'+90y=0,y(1)=9,y^'(1)=2

100 y^{^{''}} + 60 y^{^{'}} + 90 y = 0, y (1) = 9, y^{^{'}} (1) = 2

x^{'''}+9*x^{''}+x^'+9x=0

x^{^{'''}} + 9 \cdot x^{^{''}} + x^{^{'}} + 9 x = 0

(D^3-3D^2-10D)y=0

(D^{3} - 3 D^{2} - 10 D) y = 0

y^{''}+3y^'-y=0,y(1)=2,y^'(1)=0

y^{^{''}} + 3 y^{^{'}} - y = 0, y (1) = 2, y^{^{'}} (1) = 0