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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

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

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

y^{''}-y^'-12y=0,y(0)=5,y^'(0)=-1

y^{^{''}} - y^{^{'}} - 12 y = 0, y (0) = 5, y^{^{'}} (0) = - 1

x^{''}+5x^{''}+6x=0

x^{^{''}} + 5 x^{^{''}} + 6 x = 0

y^{''''}-2y^{'''}-7y^{''}=0

y^{^{''''}} - 2 y^{^{'''}} - 7 y^{^{''}} = 0

y^{''}+2y^'+y=0,y(0)=5,y(0)=-3

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 5, y (0) = - 3