y^{''}+9y=x^2sin(4x)

解

y^{^{''}} + 9 y = x^{2} sin (4 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x ^{2} sin ( 4 x )}{7} - \frac{16 x cos ( 4 x )}{49} + \frac{114}{343} sin (4 x)

解答ステップ

y^{''} (x) + 9 y = x^{2} sin (4 x)

線形 ODE を解く:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x ^{2} sin ( 4 x )}{7} - \frac{16 x cos ( 4 x )}{49} + \frac{114}{343} sin (4 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x ^{2} sin ( 4 x )}{7} - \frac{16 x cos ( 4 x )}{49} + \frac{114}{343} sin (4 x)