ODE
\[ f\left (y'(x)\right )+x y'(x)=y(x) \] ODE Classification
[_Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.00480011 (sec), leaf count = 13
\[\left \{\left \{y(x)\to f\left (c_1\right )+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) =f \left ( {\it \_C1} \right ) +{\it \_C1}\,x,[x \left ( {\it \_T} \right ) =-{\frac {\rm d}{{\rm d}{\it \_T}}}f \left ( {\it \_T} \right ) ,y \left ( {\it \_T} \right ) =-{\it \_T}\,{\frac {\rm d}{{\rm d}{\it \_T}}}f \left ( {\it \_T} \right ) +f \left ( {\it \_T} \right ) ] \right \} \] Mathematica raw input
DSolve[f[y'[x]] + x*y'[x] == y[x],y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + f[C[1]]}}
Maple raw input
dsolve(f(diff(y(x),x))+x*diff(y(x),x) = y(x), y(x),'implicit')
Maple raw output
[x(_T) = -diff(f(_T),_T), y(_T) = -_T*diff(f(_T),_T)+f(_T)], y(x) = f(_C1)+_C1*x