y^{''}+5y^'=(4t-2)sin(2t)

解

y^{^{''}} + 5 y^{^{'}} = (4 t - 2) sin (2 t)

y = c_{1} + c_{2} e^{- 5 t} - \frac{4 t sin ( 2 t )}{29} - \frac{10 t cos ( 2 t )}{29} + \frac{243}{841} sin (2 t) + \frac{129}{841} cos (2 t)

解答ステップ

y^{''} (t) + 5 y^{'} (t) = (4 t - 2) sin (2 t)

線形 ODE を解く:

y = c_{1} + c_{2} e^{- 5 t} - \frac{4 t sin ( 2 t )}{29} - \frac{10 t cos ( 2 t )}{29} + \frac{243}{841} sin (2 t) + \frac{129}{841} cos (2 t)

y = c_{1} + c_{2} e^{- 5 t} - \frac{4 t sin ( 2 t )}{29} - \frac{10 t cos ( 2 t )}{29} + \frac{243}{841} sin (2 t) + \frac{129}{841} cos (2 t)