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Beliebt Rechnen >

12x^{''}+6x^'+18x=0

Lösung

12 x^{^{''}} + 6 x^{^{'}} + 18 x = 0

Lösung

x = e^{- \frac{t}{4}} (c_{1} cos (\frac{23 t}{4}) + c_{2} sin (\frac{23 t}{4}))

Schritte zur Lösung

12 x^{''} (t) + 6 x^{'} (t) + 18 x = 0

Solve linear ODE:

x = e^{- \frac{t}{4}} (c_{1} cos (\frac{23 t}{4}) + c_{2} sin (\frac{23 t}{4}))

x = e^{- \frac{t}{4}} (c_{1} cos (\frac{23 t}{4}) + c_{2} sin (\frac{23 t}{4}))

Graph

Beliebte Beispiele

b*y=(a-v^2)y^{''}

b \cdot y = (a - v^{2}) y^{^{''}}

y^{''}=9y^'-20y

y^{^{''}} = 9 y^{^{'}} - 20 y

y^{''}-4y^{''}-5y=0

y^{^{''}} - 4 y^{^{''}} - 5 y = 0

0.25x^{''}+sqrt(2)x^'+2x=0

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

y^{''}-5y^'-14y=0,y(0)=α,y^'(0)=-14

y^{^{''}} - 5 y^{^{'}} - 14 y = 0, y (0) = α, y^{^{'}} (0) = - 14