y^{''}+y=\H(t)

解

y^{^{''}} + y = H (t)

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) H (t) d t + sin (t) \cdot \int cos (t) H (t) d t

解答ステップ

y^{''} (t) + y = H (t)

線形 ODE を解く:

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) H (t) d t + sin (t) \cdot \int cos (t) H (t) d t

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) H (t) d t + sin (t) \cdot \int cos (t) H (t) d t