y^{'''}+64y^'=tan(8x)

解

y^{^{'''}} + 64 y^{^{'}} = tan (8 x)

y = c_{1} + c_{2} cos (8 x) + c_{3} sin (8 x) + \frac{- ln ( cos ( 8 x ) ) + cos ^{2} ( 8 x ) - sin ( 8 x ) ( ln ( tan ( 8 x ) + sec ( 8 x ) ) - sin ( 8 x ) )}{512}

解答ステップ

y^{'''} (x) + 64 y^{'} (x) = tan (8 x)

線形 ODE を解く:

y = c_{1} + c_{2} cos (8 x) + c_{3} sin (8 x) + \frac{- ln ( cos ( 8 x ) ) + cos ^{2} ( 8 x ) - sin ( 8 x ) ( ln ( tan ( 8 x ) + sec ( 8 x ) ) - sin ( 8 x ) )}{512}

y = c_{1} + c_{2} cos (8 x) + c_{3} sin (8 x) + \frac{- ln ( cos ( 8 x ) ) + cos ^{2} ( 8 x ) - sin ( 8 x ) ( ln ( tan ( 8 x ) + sec ( 8 x ) ) - sin ( 8 x ) )}{512}