#### 2.70   ODE No. 70

$y'(x)-\sqrt {\frac {\text {a0}+\text {a1} x+\text {a2} x^2+\text {a3} x^3+\text {a4} x^4}{\text {b0}+\text {b1} y(x)+\text {b2} y(x)^2+\text {b3} y(x)^3+\text {b4} y(x)^4}}=0$ Mathematica : cpu = 12.6908 (sec), leaf count = 81

$\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {\#1}}\sqrt {\text {b4} K[1]^4+\text {b3} K[1]^3+\text {b2} K[1]^2+\text {b1} K[1]+\text {b0}}dK[1]\& \right ]\left [\int _1^x\sqrt {\text {a4} K[2]^4+\text {a3} K[2]^3+\text {a2} K[2]^2+\text {a1} K[2]+\text {a0}}dK[2]+c_1\right ]\right \}\right \}$ Maple : cpu = 0.124 (sec), leaf count = 113

$\left \{ \int ^{y \left ( x \right ) }\!\sqrt {{{\it \_a}}^{4}{\it b4}+{{\it \_a}}^{3}{\it b3}+{{\it \_a}}^{2}{\it b2}+{\it \_a}\,{\it b1}+{\it b0}}{d{\it \_a}}+\int ^{x}\!-\sqrt {{\frac {{{\it \_a}}^{4}{\it a4}+{{\it \_a}}^{3}{\it a3}+{{\it \_a}}^{2}{\it a2}+{\it \_a}\,{\it a1}+{\it a0}}{{\it b4}\, \left ( y \left ( x \right ) \right ) ^{4}+{\it b3}\, \left ( y \left ( x \right ) \right ) ^{3}+{\it b2}\, \left ( y \left ( x \right ) \right ) ^{2}+{\it b1}\,y \left ( x \right ) +{\it b0}}}}\sqrt {{\it b4}\, \left ( y \left ( x \right ) \right ) ^{4}+{\it b3}\, \left ( y \left ( x \right ) \right ) ^{3}+{\it b2}\, \left ( y \left ( x \right ) \right ) ^{2}+{\it b1}\,y \left ( x \right ) +{\it b0}}{d{\it \_a}}+{\it \_C1}=0 \right \}$