(cos(9x))y^'-9(tan(9x))y=9sec(9x)

解

(cos (9 x)) y^{^{'}} - 9 (tan (9 x)) y = 9 sec (9 x)

y = e^{s e c (9 x)} \cdot \int \frac{9 e ^{- s e c (9 x)} sec ( 9 x )}{cos ( 9 x )} d x

解答ステップ

(cos (9 x)) y^{'} (x) - 9 (tan (9 x)) y = 9 sec (9 x)

線形 ODE を解く:

y = e^{s e c (9 x)} \cdot \int \frac{9 e ^{- s e c (9 x)} sec ( 9 x )}{cos ( 9 x )} d x

y = e^{s e c (9 x)} \cdot \int \frac{9 e ^{- s e c (9 x)} sec ( 9 x )}{cos ( 9 x )} d x