Internal problem ID [8287]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 707.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \relax (x )\right )^{2} x \left (1+y\right )^{2}}{16}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.906 (sec). Leaf size: 182
dsolve(diff(y(x),x) = 1/16*(-ln(-1+y(x))+ln(y(x)+1)+2*ln(x))^2*x*(y(x)+1)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\mathrm e}^{\RootOf \left (x^{2} {\mathrm e}^{\textit {\_Z}} \textit {\_Z}^{2}-2 x^{2} {\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}-2}{x^{2}}\right ) \textit {\_Z} +4 \ln \relax (x )^{2} x^{2} {\mathrm e}^{\textit {\_Z}}-4 \ln \relax (x ) \ln \left ({\mathrm e}^{\textit {\_Z}}-2\right ) x^{2} {\mathrm e}^{\textit {\_Z}}+\ln \left ({\mathrm e}^{\textit {\_Z}}-2\right )^{2} x^{2} {\mathrm e}^{\textit {\_Z}}-16 \,{\mathrm e}^{\textit {\_Z}}+32\right )}-1 \\ \int _{\textit {\_b}}^{y \relax (x )}\frac {1}{4 \left (\frac {x^{2} \left (\textit {\_a} +1\right ) \ln \left (\textit {\_a} -1\right )^{2}}{4}-\left (\ln \relax (x )+\frac {\ln \left (\textit {\_a} +1\right )}{2}\right ) \left (\textit {\_a} +1\right ) x^{2} \ln \left (\textit {\_a} -1\right )+\frac {x^{2} \left (\textit {\_a} +1\right ) \ln \left (\textit {\_a} +1\right )^{2}}{4}+\ln \relax (x ) x^{2} \left (\textit {\_a} +1\right ) \ln \left (\textit {\_a} +1\right )+\ln \relax (x )^{2} \left (\textit {\_a} +1\right ) x^{2}-4 \textit {\_a} +4\right ) \left (\textit {\_a} +1\right )}d \textit {\_a} -\frac {\ln \relax (x )}{16}-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.144 (sec). Leaf size: 1391
DSolve[y'[x] == (x*(2*Log[x] - Log[-1 + y[x]] + Log[1 + y[x]])^2*(1 + y[x])^2)/16,y[x],x,IncludeSingularSolutions -> True]
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