x^{''}+3x^'+2x=3(e^{(-3t)})

Lösung

x^{^{''}} + 3 x^{^{'}} + 2 x = 3 (e^{(- 3 t)})

x = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{3}{2} e^{- 3 t}

Schritte zur Lösung

x^{''} (t) + 3 x^{'} (t) + 2 x = 3 (e^{(- 3 t)})

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{3}{2} e^{- 3 t}

x = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{3}{2} e^{- 3 t}

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (2 x)

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = cos (x)

y^{^{''}} - y^{^{'}} = 3 - 2 x, y (0) = - 1, y^{^{'}} (0) = - 1

y^{^{''}} - 25 y = e^{x}

y^{^{''}} - 14 y^{^{'}} + 45 y = 360 x^{2} - 224 x + 16