ODE
\[ y''(x)^2-x y''(x)+y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00793341 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {1}{2} c_1 x \left (x-2 c_1\right )+c_2\right \}\right \}\]
Maple ✓
cpu = 0.092 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{3}}{12}}+{\it \_C1},y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{2}}{2}}-{{\it \_C1}}^{2}x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[y'[x] - x*y''[x] + y''[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x*(x - 2*C[1])*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),'implicit')
Maple raw output
y(x) = 1/12*x^3+_C1, y(x) = 1/2*_C1*x^2-_C1^2*x+_C2