y^{''}-2y^'+10y=18e^xsec(3x)

Lösung

y^{^{''}} - 2 y^{^{'}} + 10 y = 18 e^{x} sec (3 x)

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

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 10 y = 18 e^{x} sec (3 x)

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 4 y = x e^{- x}

y^{^{''}} - 4 y^{^{'}} = 64 - 6 e^{- x}

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = t^{2}

y^{^{''}} + 4 y = 3 cos (t), y (0) = 0, y^{^{'}} (0) = 0

2 y^{^{''}} + 5 y^{^{'}} - y = 9