ODE
\[ y'''(x)+f(x) y''(x)+f(x) y(x)+y'(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.0933995 (sec), leaf count = 0 , could not solve
DSolve[f[x]*y[x] + Derivative[1][y][x] + f[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.2 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) ={{\rm e}^{ix}} \left ( \int \!{{\rm e}^{-2\,ix}} \left ( \int \!{\it \_C3}\,{{\rm e}^{\int \!-f \left ( x \right ) +i\,{\rm d}x}}\,{\rm d}x+{\it \_C2} \right ) \,{\rm d}x+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[f[x]*y[x] + y'[x] + f[x]*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
DSolve[f[x]*y[x] + Derivative[1][y][x] + f[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+f(x)*diff(diff(y(x),x),x)+diff(y(x),x)+f(x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(I*x)*(Int(exp(-2*I*x)*(Int(_C3*exp(Int(-f(x)+I,x)),x)+_C2),x)+_C1)