y^{''}+16y=11sec^2(4t)

解

y^{^{''}} + 16 y = 11 sec^{2} (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 11 + 11 ln ( tan ( 4 t ) + sec ( 4 t ) ) sin ( 4 t )}{16}

解答ステップ

y^{''} (t) + 16 y = 11 sec^{2} (4 t)

線形 ODE を解く:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 11 + 11 ln ( tan ( 4 t ) + sec ( 4 t ) ) sin ( 4 t )}{16}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 11 + 11 ln ( tan ( 4 t ) + sec ( 4 t ) ) sin ( 4 t )}{16}