一阶线性 y^{'''}+y^'=sec(x)

解答

一阶线性

y^{^{'''}} + y^{^{'}} = sec (x)

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

求解步骤

y^{'''} (x) + y^{'} (x) = sec (x)

求解线性方程:

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

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