60.2.422 problem 999

Internal problem ID [11009]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 999
Date solved : Monday, January 27, 2025 at 10:41:18 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Riccati]

\begin{align*} y^{\prime }&=\frac {\left (y-x +\ln \left (1+x \right )\right )^{2}+x}{1+x} \end{align*}

Solution by Maple

Time used: 0.008 (sec). Leaf size: 36

dsolve(diff(y(x),x) = ((y(x)-x+ln(x+1))^2+x)/(x+1),y(x), singsol=all)
 
\[ y = \frac {-\ln \left (x +1\right )^{2}+\left (x -c_{1} \right ) \ln \left (x +1\right )+c_{1} x -1}{\ln \left (x +1\right )+c_{1}} \]

Solution by Mathematica

Time used: 0.337 (sec). Leaf size: 36

DSolve[D[y[x],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*}