\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{\frac {1}{\sqrt {{\it a4}\,{x}^{4}+{\it a3}\,{x}^{3}+{\it a2}\,{x}^{2}+{\it a1}\,x+{\it a0}}}}=0} \]
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{Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,1\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,4\right ]\right )^2}}}{\sqrt {\text {a0}+x (\text {a1}+x (\text {a2}+x (\text {a3}+\text {a4} x)))} \left (\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,2\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,1\right ]\right ) \left (\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,2\right ]-\text {Root}\left [\text {a4} \text {$\#$1}^4+\text {a3} \text {$\#$1}^3+\text {a2} \text {$\#$1}^2+\text {a1} \text {$\#$1}+\text {a0}\& ,4\right ]\right )}\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 30 \[ \left \{ y \left ( x \right ) =\int \!{\frac {1}{\sqrt {{\it a4}\,{x}^{4 }+{\it a3}\,{x}^{3}+{\it a2}\,{x}^{2}+{\it a1}\,x+{\it a0}}}}\,{\rm d} x+{\it \_C1} \right \} \]
Sage: cpu = 1.012 (sec), leaf count = 0 \[ \left [c + \int \frac {1}{\sqrt {a_{4} x^{4} + a_{3} x^{3} + a_{2} x^{2} + a_{1} x + a_{0}}}\,{d x}, \text {\texttt {linear}}\right ] \]