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Beliebt Rechnen >

(d^2x)/(dt^2)+3(dx)/(dt)+6x=0

Lösung

\frac{d ^{2} x}{d t ^{2}} + 3 \frac{d x}{d t} + 6 x = 0

Lösung

x = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{15 t}{2}) + c_{2} sin (\frac{15 t}{2}))

Schritte zur Lösung

\frac{d ^{2} x}{d t ^{2}} + 3 \frac{d x}{d t} + 6 x = 0

Solve linear ODE:

x = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{15 t}{2}) + c_{2} sin (\frac{15 t}{2}))

x = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{15 t}{2}) + c_{2} sin (\frac{15 t}{2}))

Graph

Beliebte Beispiele

2y^{''}+4y^'+2y=0

2 y^{^{''}} + 4 y^{^{'}} + 2 y = 0

y^{''}-5y^'+6y=0,y(0)=2,y^'(0)=3

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 3

4(d^2x)/(dt^2)+12(dx)/(dt)+9x=0

4 \frac{d ^{2} x}{d t ^{2}} + 12 \frac{d x}{d t} + 9 x = 0

y^{''''}+2y^{'''}+2y^{''}=0

y^{^{''''}} + 2 y^{^{'''}} + 2 y^{^{''}} = 0

9y^{''}+6y^'+82y=0,y(0)=2

9 y^{^{''}} + 6 y^{^{'}} + 82 y = 0, y (0) = 2