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 = 0.0322549 (sec), leaf count = 43
\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {\sec ^2(x) \left (c_1+2 \sin (x)\right )}}\right \},\left \{y(x)\to \frac {1}{\sqrt {\sec ^2(x) \left (c_1+2 \sin (x)\right )}}\right \}\right \}\]
Maple ✓
cpu = 0.034 (sec), leaf count = 21
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{-2}+{\frac {-{\it \_C1}-2\,\sin \left ( x \right ) }{ \left ( \cos \left ( x \right ) \right ) ^{2}}}=0 \right \} \] 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),'implicit')
Maple raw output
1/y(x)^2+(-_C1-2*sin(x))/cos(x)^2 = 0