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 = 0.243351 (sec), leaf count = 84
\[\left \{\left \{y(x)\to c_3 e^{i x} \int _1^xe^{-2 i K[3]} \int _1^{K[3]}\exp \left (\int _1^{K[2]}(i-f(K[1]))dK[1]\right )dK[2]dK[3]+c_1 e^{i x}+\frac {1}{2} i c_2 e^{-i x}\right \}\right \}\]
Maple ✓
cpu = 0.764 (sec), leaf count = 36
\[[y \left (x \right ) = {\mathrm e}^{i x} \left (\int {\mathrm e}^{-2 i x} \left (\int \textit {\_C3} \,{\mathrm e}^{\int \left (i-f \left (x \right )\right )d x}d x +\textit {\_C2} \right )d x +\textit {\_C1} \right )]\] Mathematica raw input
DSolve[f[x]*y[x] + y'[x] + f[x]*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(I*x)*C[1] + ((I/2)*C[2])/E^(I*x) + E^(I*x)*C[3]*Inactive[Integrate][Inactive[Integrate][E^Inactive[Integrate][I - f[K[1]], {K[1], 1, K[2]}], {K[2], 1, K[3]}]/E^((2*I)*K[3]), {K[3], 1, 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))
Maple raw output
[y(x) = exp(I*x)*(Int(exp(-2*I*x)*(Int(_C3*exp(Int(I-f(x),x)),x)+_C2),x)+_C1)]