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

解

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

y = c_{1} cos (x) + c_{2} sin (x) + x (c_{3} cos (x) + c_{4} sin (x)) + \frac{1}{9} cos (2 x) + 5

解答ステップ

y^{(4)} (x) + 2 y^{''} (x) + y = cos (2 x) + 5

線形 ODE を解く:

y = c_{1} cos (x) + c_{2} sin (x) + x (c_{3} cos (x) + c_{4} sin (x)) + \frac{1}{9} cos (2 x) + 5

y = c_{1} cos (x) + c_{2} sin (x) + x (c_{3} cos (x) + c_{4} sin (x)) + \frac{1}{9} cos (2 x) + 5