Internal problem ID [9333]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 999.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Riccati]
\[ \boxed {y^{\prime }-\frac {\left (y-x +\ln \left (x +1\right )\right )^{2}+x}{x +1}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve(diff(y(x),x) = ((y(x)-x+ln(x+1))^2+x)/(x+1),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\ln \left (x +1\right )^{2}+\left (x -c_{1} \right ) \ln \left (x +1\right )+c_{1} x -1}{\ln \left (x +1\right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.323 (sec). Leaf size: 36
DSolve[y'[x] == (x + (-x + Log[1 + x] + y[x])^2)/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\log (x+1)+\frac {1}{-\log (x+1)+c_1} \\ y(x)\to x-\log (x+1) \\ \end{align*}