y^{'''}+169y^'=tan(13x)

解

y^{^{'''}} + 169 y^{^{'}} = tan (13 x)

y = c_{1} + c_{2} cos (13 x) + c_{3} sin (13 x) + \frac{- ln ( cos ( 13 x ) ) + cos ^{2} ( 13 x ) - sin ( 13 x ) ( ln ( tan ( 13 x ) + sec ( 13 x ) ) - sin ( 13 x ) )}{2197}

解答ステップ

y^{'''} (x) + 169 y^{'} (x) = tan (13 x)

線形 ODE を解く:

y = c_{1} + c_{2} cos (13 x) + c_{3} sin (13 x) + \frac{- ln ( cos ( 13 x ) ) + cos ^{2} ( 13 x ) - sin ( 13 x ) ( ln ( tan ( 13 x ) + sec ( 13 x ) ) - sin ( 13 x ) )}{2197}

y = c_{1} + c_{2} cos (13 x) + c_{3} sin (13 x) + \frac{- ln ( cos ( 13 x ) ) + cos ^{2} ( 13 x ) - sin ( 13 x ) ( ln ( tan ( 13 x ) + sec ( 13 x ) ) - sin ( 13 x ) )}{2197}