\[ y'(x)^3+x y'(x)^2-y(x)=0 \] ✓ Mathematica : cpu = 33.3651 (sec), leaf count = 1758
DSolve[-y[x] + x*Derivative[1][y][x]^2 + Derivative[1][y][x]^3 == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{2} \left (\frac {4\ 2^{2/3} x^4}{3 \left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}+\frac {4 \sqrt [3]{2} x^3}{3 \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}+\frac {8\ 2^{2/3} x^3}{\left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}+\frac {6 \sqrt [3]{2} x^2}{\sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}+\frac {18\ 2^{2/3} x^2}{\left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}-\frac {x^2}{3}+\frac {1}{3} 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54} x-\frac {\sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54} x}{3 \sqrt [3]{2}}+\frac {9 \sqrt [3]{2} x}{\sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}+\frac {18\ 2^{2/3} x}{\left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}+x+2 c_1+\frac {\left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}{12\ 2^{2/3}}+\frac {\sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{2 \sqrt [3]{2}}+\frac {9}{2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}+\frac {27}{2 \sqrt [3]{2} \left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}+\frac {9}{4}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (3 \left (\frac {1}{6} (3-2 x)-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{12 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (-4 x^2-12 x-9\right )}{6\ 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}\right ){}^2+4 x \left (\frac {1}{6} (3-2 x)-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{12 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (-4 x^2-12 x-9\right )}{6\ 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}\right )-2 x+2 c_1\right )\right \},\left \{y(x)\to \frac {1}{2} \left (3 \left (\frac {1}{6} (3-2 x)-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{12 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (-4 x^2-12 x-9\right )}{6\ 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}\right ){}^2+4 x \left (\frac {1}{6} (3-2 x)-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{12 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (-4 x^2-12 x-9\right )}{6\ 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}\right )-2 x+2 c_1\right )\right \}\right \}\] ✓ Maple : cpu = 0.048 (sec), leaf count = 1251
dsolve(diff(y(x),x)^3+x*diff(y(x),x)^2-y(x)=0,y(x))
\[y \left (x \right ) = 0\]