2.68   ODE No. 68

$y'(x)-\sqrt {\frac {a y(x)^4+b y(x)^2+1}{a x^4+b x^2+1}}=0$ Mathematica : cpu = 0.714945 (sec), leaf count = 373

$\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {i \sqrt {\frac {2 \text {\#1}^2 a+\sqrt {b^2-4 a}+b}{\sqrt {b^2-4 a}+b}} \sqrt {\frac {2 \text {\#1}^2 a}{b-\sqrt {b^2-4 a}}+1} F\left (i \sinh ^{-1}\left (\sqrt {2} \sqrt {\frac {a}{b+\sqrt {b^2-4 a}}} \text {\#1}\right )|\frac {b+\sqrt {b^2-4 a}}{b-\sqrt {b^2-4 a}}\right )}{\sqrt {2} \sqrt {\frac {a}{\sqrt {b^2-4 a}+b}} \sqrt {\text {\#1}^4 a+\text {\#1}^2 b+1}}\& \right ]\left [c_1-\frac {i \sqrt {\frac {\sqrt {b^2-4 a}+2 a x^2+b}{\sqrt {b^2-4 a}+b}} \sqrt {\frac {2 a x^2}{b-\sqrt {b^2-4 a}}+1} F\left (i \sinh ^{-1}\left (\sqrt {2} \sqrt {\frac {a}{b+\sqrt {b^2-4 a}}} x\right )|\frac {b+\sqrt {b^2-4 a}}{b-\sqrt {b^2-4 a}}\right )}{\sqrt {2} \sqrt {\frac {a}{\sqrt {b^2-4 a}+b}} \sqrt {a x^4+b x^2+1}}\right ]\right \}\right \}$ Maple : cpu = 0.048 (sec), leaf count = 77

$\left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {{{\it \_a}}^{4}a+{{\it \_a}}^{2}b+1}}}{d{\it \_a}}+\int ^{x}\!-{1\sqrt {{\frac {a \left ( y \left ( x \right ) \right ) ^{4}+b \left ( y \left ( x \right ) \right ) ^{2}+1}{{{\it \_a}}^{4}a+{{\it \_a}}^{2}b+1}}}{\frac {1}{\sqrt {a \left ( y \left ( x \right ) \right ) ^{4}+b \left ( y \left ( x \right ) \right ) ^{2}+1}}}}{d{\it \_a}}+{\it \_C1}=0 \right \}$