4.3.13 \(g(x) \sin (a y(x))+h(x) \cos (a y(x))+f(x)+y'(x)=0\)

ODE
\[ g(x) \sin (a y(x))+h(x) \cos (a y(x))+f(x)+y'(x)=0 \] ODE Classification

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

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 25.1185 (sec), leaf count = 0 , could not solve

DSolve[f[x] + Cos[a*y[x]]*h[x] + g[x]*Sin[a*y[x]] + Derivative[1][y][x] == 0, y[x], x]

Maple
cpu = 1.253 (sec), leaf count = 0 , could not solve

dsolve(diff(y(x),x)+f(x)+g(x)*sin(a*y(x))+h(x)*cos(a*y(x)) = 0, y(x),'implicit')

Mathematica raw input

DSolve[f[x] + Cos[a*y[x]]*h[x] + g[x]*Sin[a*y[x]] + y'[x] == 0,y[x],x]

Mathematica raw output

DSolve[f[x] + Cos[a*y[x]]*h[x] + g[x]*Sin[a*y[x]] + Derivative[1][y][x] == 0, y[
x], x]

Maple raw input

dsolve(diff(y(x),x)+f(x)+g(x)*sin(a*y(x))+h(x)*cos(a*y(x)) = 0, y(x),'implicit')

Maple raw output

dsolve(diff(y(x),x)+f(x)+g(x)*sin(a*y(x))+h(x)*cos(a*y(x)) = 0, y(x),'implicit')