##### 4.2.42 $$y'(x)+y(x)^3 \tan (x) \sec (x)=0$$

ODE
$y'(x)+y(x)^3 \tan (x) \sec (x)=0$ ODE Classiﬁcation

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.378393 (sec), leaf count = 44

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

Maple
cpu = 0.03 (sec), leaf count = 48

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

DSolve[Sec[x]*Tan[x]*y[x]^3 + y'[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(y(x),x)+y(x)^3*sec(x)*tan(x) = 0, y(x))

Maple raw output

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