ODE
\[ y''(x)^2-x y''(x)+y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.150536 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {c_1 x^2}{2}-c_1{}^2 x+c_2\right \}\right \}\]
Maple ✓
cpu = 1.476 (sec), leaf count = 28
\[\left [y \left (x \right ) = \frac {x^{3}}{12}+\textit {\_C1}, y \left (x \right ) = \frac {1}{2} x^{2} \textit {\_C1} -\textit {\_C1}^{2} x +\textit {\_C2}\right ]\] Mathematica raw input
DSolve[y'[x] - x*y''[x] + y''[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^2*C[1])/2 - x*C[1]^2 + C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)^2-x*diff(diff(y(x),x),x)+diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = 1/12*x^3+_C1, y(x) = 1/2*x^2*_C1-_C1^2*x+_C2]