y^{'''}+4y^'=cot(2x)

解

y^{^{'''}} + 4 y^{^{'}} = cot (2 x)

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

解答ステップ

y^{'''} (x) + 4 y^{'} (x) = cot (2 x)

線形 ODE を解く:

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

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