y^{'''}+y^'=sec(t),y^{'''}(0)=-2

解

y^{^{'''}} + y^{^{'}} = sec (t), y^{^{'''}} (0) = - 2

y = c_{1} + c_{2} cos (t) + 3 sin (t) + ln (tan (t) + sec (t)) - t cos (t) + ln (cos (t)) sin (t)

解答ステップ

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

線形 ODE を解く:

y = c_{1} + c_{2} cos (t) + 3 sin (t) + ln (tan (t) + sec (t)) - t cos (t) + ln (cos (t)) sin (t)

y = c_{1} + c_{2} cos (t) + 3 sin (t) + ln (tan (t) + sec (t)) - t cos (t) + ln (cos (t)) sin (t)