4.15.45 \(y'(x) \left (x^2 \sec ^2(y(x))-6 x y(x)+2\right )-3 y(x)^2+2 x \tan (y(x))=0\)

ODE
\[ y'(x) \left (x^2 \sec ^2(y(x))-6 x y(x)+2\right )-3 y(x)^2+2 x \tan (y(x))=0 \] ODE Classification

[_exact]

Book solution method
Exact equation

Mathematica
cpu = 0.122084 (sec), leaf count = 27

\[\text {Solve}\left [c_1+6 x y(x)^2=2 x^2 \tan (y(x))+4 y(x),y(x)\right ]\]

Maple
cpu = 0.081 (sec), leaf count = 23

\[ \left \{ \tan \left (y \relax (x ) \right ) {x}^{2}-3\,x \left (y \relax (x ) \right ) ^{2}+2\,y \relax (x ) +{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[2*x*Tan[y[x]] - 3*y[x]^2 + (2 + x^2*Sec[y[x]]^2 - 6*x*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

Solve[C[1] + 6*x*y[x]^2 == 2*x^2*Tan[y[x]] + 4*y[x], y[x]]

Maple raw input

dsolve((2-6*x*y(x)+x^2*sec(y(x))^2)*diff(y(x),x)+2*x*tan(y(x))-3*y(x)^2 = 0, y(x),'implicit')

Maple raw output

tan(y(x))*x^2-3*x*y(x)^2+2*y(x)+_C1 = 0