y^{''}+2y^'+4y=111e^{2t}cos(3t)

Lösung

y^{^{''}} + 2 y^{^{'}} + 4 y = 111 e^{2 t} cos (3 t)

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

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 4 y = 111 e^{2 t} cos (3 t)

Solve linear ODE:

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

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

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

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

y^{^{''}} - 4 y^{^{'}} + 4 y = 3 e^{2 x}

y^{^{''}} + y^{^{'}} = 7

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{2 t} + 2 sin (t)