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 = 0.150599 (sec), leaf count = 13
\[\{\{y(x)\to f(c_1)+c_1 x\}\}\]
Maple ✓
cpu = 0.163 (sec), leaf count = 33
\[[[x \left (\textit {\_T} \right ) = -\frac {d}{d \textit {\_T}}f \left (\textit {\_T} \right ), y \left (\textit {\_T} \right ) = -\textit {\_T} \left (\frac {d}{d \textit {\_T}}f \left (\textit {\_T} \right )\right )+f \left (\textit {\_T} \right )], y \left (x \right ) = f \left (\textit {\_C1} \right )+\textit {\_C1} x]\] 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))
Maple raw output
[[x(_T) = -diff(f(_T),_T), y(_T) = -_T*diff(f(_T),_T)+f(_T)], y(x) = f(_C1)+_C1*x]