y^{''}+2y^'+2y=4e^{-x}ln(x)

Lösung

y^{^{''}} + 2 y^{^{'}} + 2 y = 4 e^{- x} ln (x)

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) - 4 e^{- x} cos (x) (- ln (x) cos (x) + Ci (x)) + 4 e^{- x} sin (x) (ln (x) sin (x) - Si (x))

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 2 y = 4 e^{- x} ln (x)

Solve linear ODE:

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) - 4 e^{- x} cos (x) (- ln (x) cos (x) + Ci (x)) + 4 e^{- x} sin (x) (ln (x) sin (x) - Si (x))

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) - 4 e^{- x} cos (x) (- ln (x) cos (x) + Ci (x)) + 4 e^{- x} sin (x) (ln (x) sin (x) - Si (x))

y^{^{''}} + 3 y^{^{'}} = 8 x + 5

y^{^{''}} + 2 y^{^{'}} + y = 4 e^{- x} ln (x)

3 y^{^{''}} + 8 y^{^{'}} - 3 y = 8 - 3 t

2 y^{^{''}} + 4 y = 6 t, y (0) = 4.9, y^{^{'}} (0) = 0

y^{^{''}} - 5 y^{^{'}} + 6 y = 24