ODE
\[ y''(x)=\left (x^2-y'(x)\right )^2+2 x \] ODE Classification
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.014807 (sec), leaf count = 24
\[\left \{\left \{y(x)\to -\log \left (c_1-x\right )+c_2+\frac {x^3}{3}\right \}\right \}\]
Maple ✓
cpu = 0.069 (sec), leaf count = 27
\[ \left \{ {\frac {1}{x} \left ( {\it \_C2}\,x-{{\rm e}^{{\frac {{x}^{3}}{3}}-y \left ( x \right ) }}-{\it \_C1} \right ) }=0 \right \} \] Mathematica raw input
DSolve[y''[x] == 2*x + (x^2 - y'[x])^2,y[x],x]
Mathematica raw output
{{y[x] -> x^3/3 + C[2] - Log[-x + C[1]]}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = 2*x+(x^2-diff(y(x),x))^2, y(x),'implicit')
Maple raw output
(_C2*x-exp(1/3*x^3-y(x))-_C1)/x = 0