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 = 22.3974 (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 = 0.729 (sec), leaf count = 0 , could not solve
dsolve(diff(y(x),x)+f(x)+g(x)*tan(y(x)) = 0, y(x))
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))
Maple raw output
dsolve(diff(y(x),x)+f(x)+g(x)*tan(y(x)) = 0, y(x))