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 = 0.271776 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {x^3}{3}-\log (-x+c_1)+c_2\right \}\right \}\]
Maple ✓
cpu = 0.265 (sec), leaf count = 20
\[\left [y \left (x \right ) = \frac {x^{3}}{3}-\ln \left (\textit {\_C2} x -\textit {\_C1} \right )\right ]\] 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))
Maple raw output
[y(x) = 1/3*x^3-ln(_C2*x-_C1)]