(d^2y)/(dx^2)+4y=tan(2x)

解

\frac{d ^{2} y}{d x ^{2}} + 4 y = tan (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{- 2 cos ( 2 x ) ( ln ( tan ( 2 x ) + sec ( 2 x ) ) - sin ( 2 x ) ) - sin ( 4 x )}{8}

解答ステップ

\frac{d ^{2} y}{d x ^{2}} + 4 y = tan (2 x)

線形 ODE を解く:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{- 2 cos ( 2 x ) ( ln ( tan ( 2 x ) + sec ( 2 x ) ) - sin ( 2 x ) ) - sin ( 4 x )}{8}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{- 2 cos ( 2 x ) ( ln ( tan ( 2 x ) + sec ( 2 x ) ) - sin ( 2 x ) ) - sin ( 4 x )}{8}