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Beliebt Rechnen >

y^{'''}+12y^{''}+45y^'=0

Lösung

y^{^{'''}} + 12 y^{^{''}} + 45 y^{^{'}} = 0

Lösung

y = c_{1} + e^{- 6 t} (c_{2} cos (3 t) + c_{3} sin (3 t))

Schritte zur Lösung

y^{'''} (t) + 12 y^{''} (t) + 45 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + e^{- 6 t} (c_{2} cos (3 t) + c_{3} sin (3 t))

y = c_{1} + e^{- 6 t} (c_{2} cos (3 t) + c_{3} sin (3 t))

Graph

Beliebte Beispiele

y^{''}+4y=0,y(pi/6)=4,y^'(pi/6)=-8

y^{^{''}} + 4 y = 0, y (\frac{π}{6}) = 4, y^{^{'}} (\frac{π}{6}) = - 8

y^{''}-8y^'=20y,y(0)=0,y^'(0)=0

y^{^{''}} - 8 y^{^{'}} = 20 y, y (0) = 0, y^{^{'}} (0) = 0

y^{'''}-3y^{''}-9y^'-5y=0

y^{^{'''}} - 3 y^{^{''}} - 9 y^{^{'}} - 5 y = 0

3y^{''}-16y^'+13y=0

3 y^{^{''}} - 16 y^{^{'}} + 13 y = 0

y^{''}+n^2y=0,y(0)=c,y^'(0)=v

y^{^{''}} + n^{2} y = 0, y (0) = c, y^{^{'}} (0) = v