y^{''}+2y^'=(8t-7)sin(3t)

解

y^{^{''}} + 2 y^{^{'}} = (8 t - 7) sin (3 t)

y = c_{1} + c_{2} e^{- 2 t} - \frac{8 t sin ( 3 t )}{13} - \frac{16 t cos ( 3 t )}{39} + \frac{1315}{1521} sin (3 t) + \frac{38}{507} cos (3 t)

解答ステップ

y^{''} (t) + 2 y^{'} (t) = (8 t - 7) sin (3 t)

線形 ODE を解く:

y = c_{1} + c_{2} e^{- 2 t} - \frac{8 t sin ( 3 t )}{13} - \frac{16 t cos ( 3 t )}{39} + \frac{1315}{1521} sin (3 t) + \frac{38}{507} cos (3 t)

y = c_{1} + c_{2} e^{- 2 t} - \frac{8 t sin ( 3 t )}{13} - \frac{16 t cos ( 3 t )}{39} + \frac{1315}{1521} sin (3 t) + \frac{38}{507} cos (3 t)