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Beliebt Rechnen >

25x^{''}+50x^'+169x=0,x(0)=3,x^'(0)=14

Lösung

25 x^{^{''}} + 50 x^{^{'}} + 169 x = 0, x (0) = 3, x^{^{'}} (0) = 14

Lösung

x = e^{- t} (3 cos (\frac{12 t}{5}) + \frac{85}{12} sin (\frac{12 t}{5}))

Schritte zur Lösung

25 x^{''} (t) + 50 x^{'} (t) + 169 x = 0

Solve linear ODE:

x = e^{- t} (3 cos (\frac{12 t}{5}) + \frac{85}{12} sin (\frac{12 t}{5}))

x = e^{- t} (3 cos (\frac{12 t}{5}) + \frac{85}{12} sin (\frac{12 t}{5}))

Graph

Beliebte Beispiele

y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=6

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = 6

y^{^{''}} + 128 y = 0

x^{^{''}} = r^{2} x

y^{''}-8y^'+16y=0,y(0)=4,y^'(0)=7

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = 7

y^{''}+6y^'+5y=0,y(0)=0

y^{^{''}} + 6 y^{^{'}} + 5 y = 0, y (0) = 0