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)]