Internal problem ID [8495]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 917.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
\[ \boxed {y^{\prime }-\frac {y \left (\ln \left (x \right ) x +\ln \left (x \right )+\ln \left (y\right ) x +\ln \left (y\right )-x -1+\ln \left (x \right )^{2} x +2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}\right )}{x \left (x +1\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x) = y(x)*(x*ln(x)+ln(x)+ln(y(x))*x+ln(y(x))-x-1+x*ln(x)^2+2*x*ln(y(x))*ln(x)+x*ln(y(x))^2)/x/(x+1),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {\ln \left (x \right ) \ln \left (x +1\right )+c_{1} \ln \left (x \right )-\ln \left (x \right ) x -x}{\ln \left (x +1\right )+c_{1} -x}} \]
✓ Solution by Mathematica
Time used: 0.464 (sec). Leaf size: 32
DSolve[y'[x] == ((-1 - x + Log[x] + x*Log[x] + x*Log[x]^2 + Log[y[x]] + x*Log[y[x]] + 2*x*Log[x]*Log[y[x]] + x*Log[y[x]]^2)*y[x])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\frac {x}{-x+\log (x+1)+c_1}}}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}