x^{''}-2x^'+2x=e^{-t}cos(2t)

Lösung

x^{^{''}} - 2 x^{^{'}} + 2 x = e^{- t} cos (2 t)

x = e^{t} (c_{1} cos (t) + c_{2} sin (t)) - \frac{8}{65} e^{- t} sin (2 t) + \frac{1}{65} e^{- t} cos (2 t)

Schritte zur Lösung

x^{''} (t) - 2 x^{'} (t) + 2 x = e^{- t} cos (2 t)

Solve linear ODE:

x = e^{t} (c_{1} cos (t) + c_{2} sin (t)) - \frac{8}{65} e^{- t} sin (2 t) + \frac{1}{65} e^{- t} cos (2 t)

x = e^{t} (c_{1} cos (t) + c_{2} sin (t)) - \frac{8}{65} e^{- t} sin (2 t) + \frac{1}{65} e^{- t} cos (2 t)

y^{^{''}} - y^{^{'}} - 2 y = 1, y (0) = 1, y^{^{'}} (0) = 2

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + y = x

y^{^{''}} - y^{^{'}} - 6 y = 32 sin (3 x)

y^{^{''}} - 2 y^{^{'}} + y = 576 e^{9 t}

y^{^{''}} - y = - 2 t + 3