2.677   ODE No. 677

\[ y'(x)=\frac {a x^4+a x^3+a x^3 \log (x+1)-x^2 y(x)^2-x y(x)^2+y(x)-x y(x)^2 \log (x+1)}{x} \] Mathematica : cpu = 0.181987 (sec), leaf count = 80


\[\left \{\left \{y(x)\to \sqrt {a} x \tanh \left (\frac {1}{12} \left (4 \sqrt {a} x^3+3 \sqrt {a} x^2+6 \sqrt {a} x^2 \log (x+1)+6 \sqrt {a} x-6 \sqrt {a} \log (x+1)+12 \sqrt {a} c_1\right )\right )\right \}\right \}\] Maple : cpu = 0.083 (sec), leaf count = 48


\[y \relax (x ) = \tanh \left (\frac {\sqrt {a}\, \left (6 \ln \left (1+x \right ) x^{2}+4 x^{3}+3 x^{2}-6 \ln \left (1+x \right )+12 c_{1}+6 x +9\right )}{12}\right ) x \sqrt {a}\]