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Beliebt Rechnen >

25x^{''}+50x^'+169x=0,x(0)=2,x^'(0)=6

Lösung

25 x^{^{''}} + 50 x^{^{'}} + 169 x = 0, x (0) = 2, x^{^{'}} (0) = 6

Lösung

x = e^{- t} (2 cos (\frac{12 t}{5}) + \frac{10}{3} sin (\frac{12 t}{5}))

Schritte zur Lösung

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

Solve linear ODE:

x = e^{- t} (2 cos (\frac{12 t}{5}) + \frac{10}{3} sin (\frac{12 t}{5}))

x = e^{- t} (2 cos (\frac{12 t}{5}) + \frac{10}{3} sin (\frac{12 t}{5}))

Graph

Beliebte Beispiele

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

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

3y^{''}-15y^'+4y=0

3 y^{^{''}} - 15 y^{^{'}} + 4 y = 0

1y^{''}+10y^'+25y=0,y(0)=1,y^'(0)=0

1 y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{''}+12y^'+27y=0,y(0)=1,y^'(0)=-12

y^{^{''}} + 12 y^{^{'}} + 27 y = 0, y (0) = 1, y^{^{'}} (0) = - 12

18y^{''}+9y^'-5y=0

18 y^{^{''}} + 9 y^{^{'}} - 5 y = 0