##### 4.2.41 $$y'(x)+y(x) \left (y(x)^2 \sec (x)+\tan (x)\right )=0$$

ODE
$y'(x)+y(x) \left (y(x)^2 \sec (x)+\tan (x)\right )=0$ ODE Classiﬁcation

[_Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.275998 (sec), leaf count = 43

$\left \{\left \{y(x)\to -\frac {1}{\sqrt {\sec ^2(x) (2 \sin (x)+c_1)}}\right \},\left \{y(x)\to \frac {1}{\sqrt {\sec ^2(x) (2 \sin (x)+c_1)}}\right \}\right \}$

Maple
cpu = 0.051 (sec), leaf count = 30

$\left [y \left (x \right ) = \frac {\cos \left (x \right )}{\sqrt {2 \sin \left (x \right )+\textit {\_C1}}}, y \left (x \right ) = -\frac {\cos \left (x \right )}{\sqrt {2 \sin \left (x \right )+\textit {\_C1}}}\right ]$ Mathematica raw input

DSolve[y[x]*(Tan[x] + Sec[x]*y[x]^2) + y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(1/Sqrt[Sec[x]^2*(C[1] + 2*Sin[x])])}, {y[x] -> 1/Sqrt[Sec[x]^2*(C[1]
 + 2*Sin[x])]}}

Maple raw input

dsolve(diff(y(x),x)+(tan(x)+y(x)^2*sec(x))*y(x) = 0, y(x))

Maple raw output

[y(x) = 1/(2*sin(x)+_C1)^(1/2)*cos(x), y(x) = -1/(2*sin(x)+_C1)^(1/2)*cos(x)]