x^{''}-12x^'+36x=2t+e^{6t}

解

x^{^{''}} - 12 x^{^{'}} + 36 x = 2 t + e^{6 t}

x = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{18} + \frac{1}{54} + \frac{e ^{6 t} t ^{2}}{2}

解答ステップ

x^{''} (t) - 12 x^{'} (t) + 36 x = 2 t + e^{6 t}

線形 ODE を解く:

x = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{18} + \frac{1}{54} + \frac{e ^{6 t} t ^{2}}{2}

x = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{18} + \frac{1}{54} + \frac{e ^{6 t} t ^{2}}{2}