y^{''}+2y^'+6y=e^{-2t},y(0)=2,y^'(0)=1

Lösung

y^{^{''}} + 2 y^{^{'}} + 6 y = e^{- 2 t}, y (0) = 2, y^{^{'}} (0) = 1

y = e^{- t} (\frac{11}{6} cos (5 t) + \frac{19}{6 5} sin (5 t)) + \frac{1}{6} e^{- 2 t}

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 6 y = e^{- 2 t}

Solve linear ODE:

y = e^{- t} (\frac{11}{6} cos (5 t) + \frac{19}{6 5} sin (5 t)) + \frac{1}{6} e^{- 2 t}

y = e^{- t} (\frac{11}{6} cos (5 t) + \frac{19}{6 5} sin (5 t)) + \frac{1}{6} e^{- 2 t}

y^{^{''}} + 4 y^{^{'}} + 5 y = 1, y (0) = 0, y^{^{'}} (0) = 0

10 y^{^{''}} + 45 y^{^{'}} + 2500 y = 180 cos (7 π x)

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

y^{^{'''}} + y^{^{''}} - 2 y = x e^{x} + 15

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + \frac{1}{4} y = x e^{\frac{x}{2}}