\[ y'(x)-\text {R1}\left (x,\sqrt {\text {a0}+\text {a1} x+\text {a2} x^2+\text {a3} x^3+\text {a4} x^4}\right ) \text {R2}\left (y(x),\sqrt {\text {b0}+\text {b1} y(x)+\text {b2} y(x)^2+\text {b3} y(x)^3+\text {b4} y(x)^4}\right )=0 \] ✓ Mathematica : cpu = 1.08169 (sec), leaf count = 84
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {1}{\text {R2}\left (K[1],\sqrt {\text {b1} K[1]+\text {b2} K[1]^2+\text {b3} K[1]^3+\text {b4} K[1]^4+\text {b0}}\right )} \, dK[1]\& \right ]\left [\int _1^x \text {R1}\left (K[2],\sqrt {K[2] (K[2] (K[2] (\text {a4} K[2]+\text {a3})+\text {a2})+\text {a1})+\text {a0}}\right ) \, dK[2]+c_1\right ]\right \}\right \}\]
✓ Maple : cpu = 0.013 (sec), leaf count = 64
\[ \left \{ \int \!{\it R1} \left ( x,\sqrt {{\it a4}\,{x}^{4}+{\it a3}\,{x}^{3}+{\it a2}\,{x}^{2}+{\it a1}\,x+{\it a0}} \right ) \,{\rm d}x-\int ^{y \left ( x \right ) }\! \left ( {\it R2} \left ( {\it \_a},\sqrt {{{\it \_a}}^{4}{\it b4}+{{\it \_a}}^{3}{\it b3}+{{\it \_a}}^{2}{\it b2}+{\it \_a}\,{\it b1}+{\it b0}} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1}=0 \right \} \]