\[ \left (10 x^2 y(x)^3-3 y(x)^2-2\right ) y'(x)+5 x y(x)^4+x=0 \] ✓ Mathematica : cpu = 0.204729 (sec), leaf count = 2097
\[\left \{\left \{y(x)\to -\frac {\sqrt {3} \sqrt {\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^2+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^2}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+3}{x^4}} x^2+\sqrt {3} \sqrt {-\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^4+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^4}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}-6 x^2+\frac {6 \sqrt {3} \left (100 x^4+1\right )}{\sqrt {\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^2+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^2}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+3}{x^4}}}}{x^6}} x^2-3}{30 x^2}\right \},\left \{y(x)\to \frac {-\sqrt {3} \sqrt {\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^2+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^2}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+3}{x^4}} x^2+\sqrt {3} \sqrt {-\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^4+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^4}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}-6 x^2+\frac {6 \sqrt {3} \left (100 x^4+1\right )}{\sqrt {\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^2+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^2}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+3}{x^4}}}}{x^6}} x^2+3}{30 x^2}\right \},\left \{y(x)\to \frac {\sqrt {3} \sqrt {\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^2+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^2}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+3}{x^4}} x^2-\sqrt {3} \sqrt {\frac {-5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^4-\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^4}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+6 x^2+\frac {6 \sqrt {3} \left (100 x^4+1\right )}{\sqrt {\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^2+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^2}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+3}{x^4}}}}{x^6}} x^2+3}{30 x^2}\right \},\left \{y(x)\to \frac {\sqrt {3} \sqrt {\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^2+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^2}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+3}{x^4}} x^2+\sqrt {3} \sqrt {\frac {-5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^4-\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^4}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+6 x^2+\frac {6 \sqrt {3} \left (100 x^4+1\right )}{\sqrt {\frac {5 \sqrt [3]{6} \sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}} x^2+\frac {10\ 6^{2/3} \left (5 x^4-10 c_1 x^2-2\right ) x^2}{\sqrt [3]{189 x^2-18 c_1+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}}}+3}{x^4}}}}{x^6}} x^2+3}{30 x^2}\right \}\right \}\]
✓ Maple : cpu = 0.033 (sec), leaf count = 29
\[ \left \{ {\frac {5\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}}{2}}- \left ( y \left ( x \right ) \right ) ^{3}+{\frac {{x}^{2}}{2}}-2\,y \left ( x \right ) +{\it \_C1}=0 \right \} \]