ODE
\[ f\left (y''(x)\right )+x y''(x)=y'(x) \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.160004 (sec), leaf count = 22
\[\left \{\left \{y(x)\to x f(c_1)+\frac {c_1 x^2}{2}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.045 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {x^{2} \RootOf \left (-f \left (\textit {\_Z} \right )+\textit {\_C1} \right )}{2}+\textit {\_C1} x +\textit {\_C2}\right ]\] 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))
Maple raw output
[y(x) = 1/2*x^2*RootOf(-f(_Z)+_C1)+_C1*x+_C2]