y^{''}+5y^'+2y=9t+7

Lösung

y^{^{''}} + 5 y^{^{'}} + 2 y = 9 t + 7

y = c_{1} e^{\frac{( - 5 + 17 ) t}{2}} + c_{2} e^{\frac{( - 5 - 17 ) t}{2}} + \frac{9 t}{2} - \frac{31}{4}

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) + 2 y = 9 t + 7

Solve linear ODE:

y = c_{1} e^{\frac{( - 5 + 17 ) t}{2}} + c_{2} e^{\frac{( - 5 - 17 ) t}{2}} + \frac{9 t}{2} - \frac{31}{4}

y = c_{1} e^{\frac{( - 5 + 17 ) t}{2}} + c_{2} e^{\frac{( - 5 - 17 ) t}{2}} + \frac{9 t}{2} - \frac{31}{4}

y^{^{''}} + 4 y^{^{'}} = 2

(D^{2} + 5 D + 6) y = e^{2 x}

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

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{x} (0 = (2 x))

y^{^{''}} - 6 y^{^{'}} + 9 y = 18