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

解答

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}

求解步骤

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

求解线性方程:

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}

y^{^{'''}} - 2 y^{^{''}} + 4 y^{^{'}} - 8 = 0

y^{^{''''}} - y = 12 t + cos (t)

y^{^{''}} + 2 y^{^{'}} + 2 y = x^{2} - 3 x e^{- 2 x} cos (5 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{2 x}

y^{^{''}} - 2 y^{^{'}} + 2 y = 3 x + e^{x} tan (x)