ODE
\[ f\left (y''(x)\right )+x y''(x)=y'(x) \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.015016 (sec), leaf count = 22
\[\left \{\left \{y(x)\to x f\left (c_1\right )+\frac {c_1 x^2}{2}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.167 (sec), leaf count = 24
\[ \left \{ -f \left ( {\frac {-2\,{\it \_C1}\,x-2\,{\it \_C2}+2\,y \left ( x \right ) }{{x}^{2}}} \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[f[y''[x]] + x*y''[x] == y'[x],y[x],x]
Mathematica raw output
{{y[x] -> (x^2*C[1])/2 + C[2] + x*f[C[1]]}}
Maple raw input
dsolve(f(diff(diff(y(x),x),x))+x*diff(diff(y(x),x),x) = diff(y(x),x), y(x),'implicit')
Maple raw output
-f((-2*_C1*x-2*_C2+2*y(x))/x^2)+_C1 = 0