\[ y'(x)-\sqrt {\frac {\text {a0}+\text {a1} x+\text {a2} x^2+\text {a3} x^3+\text {a4} x^4}{\text {b0}+\text {b1} y(x)+\text {b2} y(x)^2+\text {b3} y(x)^3+\text {b4} y(x)^4}}=0 \] ✓ Mathematica : cpu = 22.5065 (sec), leaf count = 81
DSolve[-Sqrt[(a0 + a1*x + a2*x^2 + a3*x^3 + a4*x^4)/(b0 + b1*y[x] + b2*y[x]^2 + b3*y[x]^3 + b4*y[x]^4)] + Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\sqrt {\text {b4} K[1]^4+\text {b3} K[1]^3+\text {b2} K[1]^2+\text {b1} K[1]+\text {b0}}dK[1]\& \right ]\left [\int _1^x\sqrt {\text {a4} K[2]^4+\text {a3} K[2]^3+\text {a2} K[2]^2+\text {a1} K[2]+\text {a0}}dK[2]+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.144 (sec), leaf count = 113
dsolve(diff(y(x),x)-((a4*x^4+a3*x^3+a2*x^2+a1*x+a0)/(b4*y(x)^4+b3*y(x)^3+b2*y(x)^2+b1*y(x)+b0))^(1/2) = 0,y(x))
\[\int _{}^{y \left (x \right )}\sqrt {\textit {\_a}^{4} \operatorname {b4} +\textit {\_a}^{3} \operatorname {b3} +\textit {\_a}^{2} \operatorname {b2} +\textit {\_a} \operatorname {b1} +\operatorname {b0}}d \textit {\_a} +\int _{}^{x}-\sqrt {\frac {\textit {\_a}^{4} \operatorname {a4} +\textit {\_a}^{3} \operatorname {a3} +\textit {\_a}^{2} \operatorname {a2} +\textit {\_a} \operatorname {a1} +\operatorname {a0}}{\operatorname {b4} y \left (x \right )^{4}+\operatorname {b3} y \left (x \right )^{3}+\operatorname {b2} y \left (x \right )^{2}+\operatorname {b1} y \left (x \right )+\operatorname {b0}}}\, \sqrt {\operatorname {b4} y \left (x \right )^{4}+\operatorname {b3} y \left (x \right )^{3}+\operatorname {b2} y \left (x \right )^{2}+\operatorname {b1} y \left (x \right )+\operatorname {b0}}d \textit {\_a} +c_{1} = 0\]