y^{''}+49y=8cos(7x)(3x+2)

解

y^{^{''}} + 49 y = 8 cos (7 x) (3 x + 2)

y = c_{1} cos (7 x) + c_{2} sin (7 x) + \frac{6 x ^{2} sin ( 7 x )}{7} + \frac{8 x sin ( 7 x )}{7} + \frac{6 x cos ( 7 x )}{49}

解答ステップ

y^{''} (x) + 49 y = 8 cos (7 x) (3 x + 2)

線形 ODE を解く:

y = c_{1} cos (7 x) + c_{2} sin (7 x) + \frac{6 x ^{2} sin ( 7 x )}{7} + \frac{8 x sin ( 7 x )}{7} + \frac{6 x cos ( 7 x )}{49}

y = c_{1} cos (7 x) + c_{2} sin (7 x) + \frac{6 x ^{2} sin ( 7 x )}{7} + \frac{8 x sin ( 7 x )}{7} + \frac{6 x cos ( 7 x )}{49}