ODE
\[ x^2 y'''(x)+x y''(x)-(1-2 x y(x)) y'(x)+y(x)^2=f(x) \] ODE Classification
[[_3rd_order, _exact, _nonlinear]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.0857774 (sec), leaf count = 0 , could not solve
DSolve[y[x]^2 - (1 - 2*x*y[x])*Derivative[1][y][x] + x*Derivative[2][y][x] + x^2*Derivative[3][y][x] == f[x], y[x], x]
Maple ✓
cpu = 0.755 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ {{\it \_a}}^{2}{\frac {{\rm d}^{2}}{{\rm d}{{\it \_a}}^{2}}}{\it \_b} \left ( {\it \_a} \right ) +{\it \_a}\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}- \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_a}-\int \!f \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}=0 \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[y[x]^2 - (1 - 2*x*y[x])*y'[x] + x*y''[x] + x^2*y'''[x] == f[x],y[x],x]
Mathematica raw output
DSolve[y[x]^2 - (1 - 2*x*y[x])*Derivative[1][y][x] + x*Derivative[2][y][x] + x^2*Derivative[3][y][x] == f[x], y[x], x]
Maple raw input
dsolve(x^2*diff(diff(diff(y(x),x),x),x)+x*diff(diff(y(x),x),x)-(1-2*x*y(x))*diff(y(x),x)+y(x)^2 = f(x), y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_b(_a),[{_a^2*diff(diff(_b(_a),_a),_a)+_a*_b(_a)^2-diff(_b(_a),_a)*_a-Int(f(_a),_a)+_C1 = 0}, {_a = x, _b(_a) = y(x)}, {x = _a, y(x) = _b(_a)}])