4.3.30 \(f(x)+g(x) \tan (y(x))+y'(x)=0\)

ODE
\[ f(x)+g(x) \tan (y(x))+y'(x)=0 \] ODE Classification

[`y=_G(x,y')`]

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 22.5539 (sec), leaf count = 0 , could not solve

DSolve[f[x] + g[x]*Tan[y[x]] + Derivative[1][y][x] == 0, y[x], x]

Maple
cpu = 0.748 (sec), leaf count = 0 , could not solve

dsolve(diff(y(x),x)+f(x)+g(x)*tan(y(x)) = 0, y(x),'implicit')

Mathematica raw input

DSolve[f[x] + g[x]*Tan[y[x]] + y'[x] == 0,y[x],x]

Mathematica raw output

DSolve[f[x] + g[x]*Tan[y[x]] + Derivative[1][y][x] == 0, y[x], x]

Maple raw input

dsolve(diff(y(x),x)+f(x)+g(x)*tan(y(x)) = 0, y(x),'implicit')

Maple raw output

dsolve(diff(y(x),x)+f(x)+g(x)*tan(y(x)) = 0, y(x),'implicit')