\[ y'(x)-\sqrt {\frac {\text {b0}+\text {b1} y(x)+\text {b2} y(x)^2+\text {b3} y(x)^3+\text {b4} y(x)^4}{\text {a0}+\text {a1} x+\text {a2} x^2+\text {a3} x^3+\text {a4} x^4}}=0 \] ✓ Mathematica : cpu = 3.74941 (sec), leaf count = 2237
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)}}\right )|\frac {\left (\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,2\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,3\right ]\right ) \left (\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,1\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,4\right ]\right )}{\left (\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,1\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,3\right ]\right ) \left (\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,2\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,4\right ]\right )}\right ) \left (x-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,2\right ]\right )^2 \sqrt {\frac {\left (\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,1\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,2\right ]\right ) \left (x-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,3\right ]\right )}{\left (x-\text {Root}\left [\text {a4} \text 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{$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,1\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,4\right ]\right )^2}}}{\sqrt {\text {a0}+x (\text {a1}+x (\text {a2}+x (\text {a3}+\text {a4} x)))} \left (\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,2\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,1\right ]\right ) \left (\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,2\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,4\right ]\right )},y(x)\right ]\] ✓ Maple : cpu = 0.129 (sec), leaf count = 113
\[\left \{c_{1}+\int _{}^{y \left (x \right )}\frac {1}{\sqrt {\textit {\_a}^{4} \mathit {b4} +\textit {\_a}^{3} \mathit {b3} +\textit {\_a}^{2} \mathit {b2} +\textit {\_a} \mathit {b1} +\mathit {b0}}}d \textit {\_a} +\int _{}^{x}-\frac {\sqrt {\frac {\mathit {b4} y \left (x \right )^{4}+\mathit {b3} y \left (x \right )^{3}+\mathit {b2} y \left (x \right )^{2}+\mathit {b1} y \left (x \right )+\mathit {b0}}{\textit {\_a}^{4} \mathit {a4} +\textit {\_a}^{3} \mathit {a3} +\textit {\_a}^{2} \mathit {a2} +\textit {\_a} \mathit {a1} +\mathit {a0}}}}{\sqrt {\mathit {b4} y \left (x \right )^{4}+\mathit {b3} y \left (x \right )^{3}+\mathit {b2} y \left (x \right )^{2}+\mathit {b1} y \left (x \right )+\mathit {b0}}}d \textit {\_a} = 0\right \}\]