y^{''}+9y=5sec(3t)

解

y^{^{''}} + 9 y = 5 sec (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{5}{9} ln (cos (3 t)) cos (3 t) + \frac{5}{3} t sin (3 t)

解答ステップ

y^{''} (t) + 9 y = 5 sec (3 t)

線形 ODE を解く:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{5}{9} ln (cos (3 t)) cos (3 t) + \frac{5}{3} t sin (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{5}{9} ln (cos (3 t)) cos (3 t) + \frac{5}{3} t sin (3 t)