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Beliebt Rechnen >

0.5x^{''}+0.5x^'+6x=0,x(0)=3,x^'(0)=0

Lösung

0.5 x^{^{''}} + 0.5 x^{^{'}} + 6 x = 0, x (0) = 3, x^{^{'}} (0) = 0

Lösung

x = e^{- \frac{t}{2}} (3 cos (\frac{47 t}{2}) + \frac{3}{47} sin (\frac{47 t}{2}))

Schritte zur Lösung

0.5 x^{''} (t) + 0.5 x^{'} (t) + 6 x = 0

Solve linear ODE:

x = e^{- \frac{t}{2}} (3 cos (\frac{47 t}{2}) + \frac{3}{47} sin (\frac{47 t}{2}))

x = e^{- \frac{t}{2}} (3 cos (\frac{47 t}{2}) + \frac{3}{47} sin (\frac{47 t}{2}))

Graph

Beliebte Beispiele

y^{^{''}} - 144 y = 0

y^{''''}+4y^{'''}+8y^{''}+16y^'+16y=0

y^{^{''''}} + 4 y^{^{'''}} + 8 y^{^{''}} + 16 y^{^{'}} + 16 y = 0

(d^2y)/(dx^2)+6(dy)/(dx)+6y=0

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

y^{'''}-17y^{''}+80y^'-100y=0

y^{^{'''}} - 17 y^{^{''}} + 80 y^{^{'}} - 100 y = 0

2y^{'''}+15y^{''}+24y^'+11y=0

2 y^{^{'''}} + 15 y^{^{''}} + 24 y^{^{'}} + 11 y = 0