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 = 12.7936 (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 = 0.174 (sec), leaf count = 113


\[\int _{}^{y \relax (x )}\sqrt {\textit {\_a}^{4} \mathit {b4} +\textit {\_a}^{3} \mathit {b3} +\textit {\_a}^{2} \mathit {b2} +\textit {\_a} \mathit {b1} +\mathit {b0}}d \textit {\_a} +\int _{}^{x}-\sqrt {\frac {\textit {\_a}^{4} \mathit {a4} +\textit {\_a}^{3} \mathit {a3} +\textit {\_a}^{2} \mathit {a2} +\textit {\_a} \mathit {a1} +\mathit {a0}}{\mathit {b4} y \relax (x )^{4}+\mathit {b3} y \relax (x )^{3}+\mathit {b2} y \relax (x )^{2}+\mathit {b1} y \relax (x )+\mathit {b0}}}\, \sqrt {\mathit {b4} y \relax (x )^{4}+\mathit {b3} y \relax (x )^{3}+\mathit {b2} y \relax (x )^{2}+\mathit {b1} y \relax (x )+\mathit {b0}}d \textit {\_a} +c_{1} = 0\]