4.42.7 $(x-y^{\prime }(x{)}^2)y^{″}(x)=x^2-y^{\prime }(x)$

ODE
$$(x-y^{\prime }(x{)}^2)y^{″}(x)=x^2-y^{\prime }(x)$$ 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

$$\{y\left(x\right)=\int \frac{1}{2}({(-4x^3+12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(-6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}+4x)\frac{1}{\sqrt[3]{-4x^3+12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(-6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2},y\left(x\right)=\int -\frac{1}{4}(-i\sqrt{3}{(-4x^3+12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(-6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}+4i\sqrt{3}x+{(-4x^3+12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(-6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}+4x)\frac{1}{\sqrt[3]{-4x^3+12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(-6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2},y\left(x\right)=\int -\frac{1}{4}(i\sqrt{3}{(-4x^3+12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(-6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}-4i\sqrt{3}x+{(-4x^3+12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(-6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2})}^{\frac{2}{3}}+4x)\frac{1}{\sqrt[3]{-4x^3+12\mathit{\_}\mathit{C}\mathit{1}+4\sqrt{x^6+(-6\mathit{\_}\mathit{C}\mathit{1}-4)x^3+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2}\}$$ 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+1
2*_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