\[ y'(x)-\sqrt {\frac {a y(x)^4+b y(x)^2+1}{a x^4+b x^2+1}}=0 \] ✓ Mathematica : cpu = 20.5135 (sec), leaf count = 373
DSolve[-Sqrt[(1 + b*y[x]^2 + a*y[x]^4)/(1 + b*x^2 + a*x^4)] + Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {i \sqrt {\frac {2 \text {$\#$1}^2 a+\sqrt {b^2-4 a}+b}{\sqrt {b^2-4 a}+b}} \sqrt {\frac {2 \text {$\#$1}^2 a}{b-\sqrt {b^2-4 a}}+1} \operatorname {EllipticF}\left (i \text {arcsinh}\left (\sqrt {2} \sqrt {\frac {a}{b+\sqrt {b^2-4 a}}} \text {$\#$1}\right ),\frac {b+\sqrt {b^2-4 a}}{b-\sqrt {b^2-4 a}}\right )}{\sqrt {2} \sqrt {\frac {a}{\sqrt {b^2-4 a}+b}} \sqrt {\text {$\#$1}^4 a+\text {$\#$1}^2 b+1}}\& \right ]\left [c_1-\frac {i \sqrt {\frac {\sqrt {b^2-4 a}+2 a x^2+b}{\sqrt {b^2-4 a}+b}} \sqrt {\frac {2 a x^2}{b-\sqrt {b^2-4 a}}+1} \operatorname {EllipticF}\left (i \text {arcsinh}\left (\sqrt {2} \sqrt {\frac {a}{b+\sqrt {b^2-4 a}}} x\right ),\frac {b+\sqrt {b^2-4 a}}{b-\sqrt {b^2-4 a}}\right )}{\sqrt {2} \sqrt {\frac {a}{\sqrt {b^2-4 a}+b}} \sqrt {a x^4+b x^2+1}}\right ]\right \}\right \}\] ✓ Maple : cpu = 0.06 (sec), leaf count = 77
dsolve(diff(y(x),x)-((a*y(x)^4+b*y(x)^2+1)/(a*x^4+b*x^2+1))^(1/2) = 0,y(x))
\[\int _{}^{y \left (x \right )}\frac {1}{\sqrt {\textit {\_a}^{4} a +\textit {\_a}^{2} b +1}}d \textit {\_a} +\int _{}^{x}-\frac {\sqrt {\frac {a y \left (x \right )^{4}+b y \left (x \right )^{2}+1}{\textit {\_a}^{4} a +\textit {\_a}^{2} b +1}}}{\sqrt {a y \left (x \right )^{4}+b y \left (x \right )^{2}+1}}d \textit {\_a} +c_{1} = 0\]