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Beliebt Rechnen >

7x^{''}+3x^'+7x=0,x(0)=-4,x^'(0)=0

Lösung

7 x^{^{''}} + 3 x^{^{'}} + 7 x = 0, x (0) = - 4, x^{^{'}} (0) = 0

Lösung

x = e^{- \frac{3 t}{14}} (- 4 cos (\frac{187 t}{14}) - \frac{12}{187} sin (\frac{187 t}{14}))

Schritte zur Lösung

7 x^{''} (t) + 3 x^{'} (t) + 7 x = 0

Solve linear ODE:

x = e^{- \frac{3 t}{14}} (- 4 cos (\frac{187 t}{14}) - \frac{12}{187} sin (\frac{187 t}{14}))

x = e^{- \frac{3 t}{14}} (- 4 cos (\frac{187 t}{14}) - \frac{12}{187} sin (\frac{187 t}{14}))

Graph

Beliebte Beispiele

y^{'''}-21y^{''}+128y^'-240y=0

y^{^{'''}} - 21 y^{^{''}} + 128 y^{^{'}} - 240 y = 0

y^{''}-6y^'+45y=0,y(0)=4,y^'(0)=-6

y^{^{''}} - 6 y^{^{'}} + 45 y = 0, y (0) = 4, y^{^{'}} (0) = - 6

24y^{''}+y^'-3y=0

24 y^{^{''}} + y^{^{'}} - 3 y = 0

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

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

20y^{''}+80y^'+100y=0

20 y^{^{''}} + 80 y^{^{'}} + 100 y = 0