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')