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 = 0.0261714 (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 = 0.012 (sec), leaf count = 15

\[ \left \{ \left (y \relax (x ) \right ) ^{-2}-2\,\sec \relax (x ) -{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/y(x)^2-2*sec(x)-_C1 = 0