y^{''}-2y^'-17y=sin(t)-cos(t)

解

y^{^{''}} - 2 y^{^{'}} - 17 y = sin (t) - cos (t)

y = c_{1} e^{(1 + 32) t} + c_{2} e^{(1 - 32) t} - \frac{2}{41} sin (t) + \frac{5}{82} cos (t)

解答ステップ

y^{''} (t) - 2 y^{'} (t) - 17 y = sin (t) - cos (t)

線形 ODE を解く:

y = c_{1} e^{(1 + 32) t} + c_{2} e^{(1 - 32) t} - \frac{2}{41} sin (t) + \frac{5}{82} cos (t)

y = c_{1} e^{(1 + 32) t} + c_{2} e^{(1 - 32) t} - \frac{2}{41} sin (t) + \frac{5}{82} cos (t)