x^{''}+6x^'-4x=8e^t

Lösung

x^{^{''}} + 6 x^{^{'}} - 4 x = 8 e^{t}

x = c_{1} e^{(- 3 + 13) t} + c_{2} e^{(- 3 - 13) t} + \frac{8}{3} e^{t}

Schritte zur Lösung

x^{''} (t) + 6 x^{'} (t) - 4 x = 8 e^{t}

Solve linear ODE:

x = c_{1} e^{(- 3 + 13) t} + c_{2} e^{(- 3 - 13) t} + \frac{8}{3} e^{t}

x = c_{1} e^{(- 3 + 13) t} + c_{2} e^{(- 3 - 13) t} + \frac{8}{3} e^{t}

y^{^{''}} + 9 y = 2 cos (3 x) - 3 sin (3 x)

y^{^{''}} - 4 y^{^{'}} + 3 = 0

y^{^{''}} + 3 y = 6 x

y^{^{''}} - 3 y^{^{'}} + 2 = 0

- 2 y^{^{''}} + 7 y^{^{'}} - y - 8 = - 6 x^{2} - 2 x^{3} e^{x}