ODE
\[ \left (x-y'(x)^2\right ) y''(x)=x^2-y'(x) \] ODE Classification
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✗
cpu = 599.997 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.14 (sec), leaf count = 330
\[ \left \{ y \left ( x \right ) =\int \!{\frac {1}{2} \left ( \left ( -4\,{x}^{3}+12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( -6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,x \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}+12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( -6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}}}}}}\,{\rm d}x+{\it \_C2},y \left ( x \right ) =\int \!-{\frac {1}{4} \left ( -i\sqrt {3} \left ( -4\,{x}^{3}+12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( -6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,i\sqrt {3}x+ \left ( -4\,{x}^{3}+12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( -6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,x \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}+12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( -6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}}}}}}\,{\rm d}x+{\it \_C2},y \left ( x \right ) =\int \!-{\frac {1}{4} \left ( i\sqrt {3} \left ( -4\,{x}^{3}+12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( -6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,i\sqrt {3}x+ \left ( -4\,{x}^{3}+12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( -6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,x \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}+12\,{\it \_C1}+4\,\sqrt {{x}^{6}+ \left ( -6\,{\it \_C1}-4 \right ) {x}^{3}+9\,{{\it \_C1}}^{2}}}}}}\,{\rm d}x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[(x - y'[x]^2)*y''[x] == x^2 - y'[x],y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve((x-diff(y(x),x)^2)*diff(diff(y(x),x),x) = x^2-diff(y(x),x), y(x),'implicit')
Maple raw output
y(x) = Int(1/2*((-4*x^3+12*_C1+4*(x^6+(-6*_C1-4)*x^3+9*_C1^2)^(1/2))^(2/3)+4*x)/(-4*x^3+12*_C1+4*(x^6+(-6*_C1-4)*x^3+9*_C1^2)^(1/2))^(1/3),x)+_C2, y(x) = Int(-1/4*(I*3^(1/2)*(-4*x^3+12*_C1+4*(x^6+(-6*_C1-4)*x^3+9*_C1^2)^(1/2))^(2/3)-4*I*3^(1/2)*x+(-4*x^3+12*_C1+4*(x^6+(-6*_C1-4)*x^3+9*_C1^2)^(1/2))^(2/3)+4*x)/(-4*x^3+12*_C1+4*(x^6+(-6*_C1-4)*x^3+9*_C1^2)^(1/2))^(1/3),x)+_C2, y(x) = Int(-1/4*(-I*3^(1/2)*(-4*x^3+12*_C1+4*(x^6+(-6*_C1-4)*x^3+9*_C1^2)^(1/2))^(2/3)+4*I*3^(1/2)*x+(-4*x^3+12*_C1+4*(x^6+(-6*_C1-4)*x^3+9*_C1^2)^(1/2))^(2/3)+4*x)/(-4*x^3+12*_C1+4*(x^6+(-6*_C1-4)*x^3+9*_C1^2)^(1/2))^(1/3),x)+_C2