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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + y = 6 e^{- 7 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} - 5 y = t e^{t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} - 12 y = x - 6

x^{^{''}} + x = cos (3 t)

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 5 + 4 sin (x)